APAB:9913001Let Determine the exact domain of f as an interval or a union of intervals.Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913002Simplify by factoring the numerator and the denominator completely over the reals and cancelling every common factor.Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913003Using exact values only, evaluate Then find all solutions of the equation 2\sin\theta=\sqrt{3} in the interval [0,2…Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913004Let f(x)=\sqrt{x-1} and g(x)=\ln(4-x^2).Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913005Let Find a formula for f^{-1}(x).Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913006Define Compute p(-3), p(0), and p(2).Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913007On the interval [-4,6], the graph of a function r consists of three line segments: the segment joining (-4,3) to (0…Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913008Selected values of a function g are given in the table below.Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913009Let where \arccos denotes the principal inverse cosine, with values in [0,\pi].Limits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913010Suppose Using only limit laws, evaluateLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913011Evaluate Show the factoring that is valid for x\neq -2, and explain why cancelling the common factor does not asser…View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913012Evaluate Explain why multiplying by a conjugate is valid here, and explain why cancelling the common factor x-7 doe…View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913013Evaluate Show the algebraic simplification that is valid for x\neq 0.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913014Evaluate using an explicit inequality and the Squeeze Theorem.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913015Evaluate using the standard limit \lim_{u\to 0}(\sin u)/u=1.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913016Evaluate using the identity 1-\cos\theta=2\sin^2(\theta/2) and the standard limit \lim_{u\to 0}(\sin u)/u=1.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913017Define Evaluate f(1), \lim_{x\to 1^-}f(x), and \lim_{x\to 1^+}f(x).View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913018Evaluate, or determine that it does not exist, Check that the expression has real domain points on both sides of zero.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913019Let Evaluate the following limits, allowing the symbols \infty and -\infty: Identify every vertical asymptote of y=…View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913020Define Find the exact real domain of g.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913021Let Evaluate \lim_{x\to\infty}R(x) and \lim_{x\to-\infty}R(x).View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913022Evaluate First identify a left-hand tail of the real line on which the expression is defined as a real number.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913023Evaluate using the substitution u=3/x and the standard limit \lim_{u\to 0}(\sin u)/u=1.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913024Evaluate In each case, account explicitly for the identity \sqrt{x^2}=|x|.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913025For a real parameter b, define Find the unique value of b for which f_b is continuous at x=3.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913026Let Identify the domain of G, every discontinuity, every vertical asymptote, any removable discontinuity (including…View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913027Let (a) Evaluate \lim_{x\to 0}f(x).View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913028Let Determine the domain of m.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913029Let p(x)=x^3+2x-1.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913030A continuous function T gives the outdoor temperature in degrees Fahrenheit t hours after 6:00 a.m., for 0\le t\le 8.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913031Let f(x)=\dfrac{1}{3x+2}.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913032Starting from the limit definition of the derivative, prove that You may use the cosine angle-addition formula and…View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913033Let f(x)=\sqrt[3]{x+8}.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913034Let f(x)=x^{5/3}, defined for every real x by f(x)=\bigl(\sqrt[3]{x}\bigr)^5.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913035For real parameters a and b, define (a) Determine all pairs (a,b) for which f is continuous at x=2.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913036For real parameters k and m, define (a) Find every pair (k,m) for which g is continuous at x=0.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913037Let h(x)=\lvert x^2-16\rvert.View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913038Let (a) Find f'(x).View access optionsLimits ContinuityAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableLimits and continuityAP Calculus AB · CalculationProgress not loaded
APAB:9913039Let (a) Find F'(x), identifying explicitly where the product rule is used and where the chain rule is used.View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913040Starting from \cot x=\dfrac{\cos x}{\sin x} and the known derivatives of sine and cosine, use the quotient rule to…View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913041Define (a) Show that the argument of the logarithm is positive for every real x.View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913042For x>4, let Use logarithmic differentiation to find y' in factored form.View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913043Differentiable functions f and g take the exact values Define (a) Compute H(1).View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913044The curve x^2+3xy+2y^2=12 contains the point (2,1).View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913045The curve x^2+y^2+xy=7 passes through (1,2).View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913046A differentiable one-to-one function f on an open interval containing 4 satisfies f(4)=-2 and f'(4)=5.View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913047Let y=\arccos x use the principal range [0,\pi].View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913048Let f be twice differentiable near x=3, with Assume f has a twice-differentiable local inverse g=f^{-1} near y=1.View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913049For x>0, let y=x^{\cos x}.View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded
APAB:9913050A twice-differentiable function f satisfies Define h(x)=e^x f(x^2).View access optionsDifferentiation Definition RulesAP Calculus AB Problem SolvingPrivateLabels unavailablePrivate saving unavailableDifferentiation definitions and fundamental rulesAP Calculus AB · CalculationProgress not loaded