Calculus I · Unit 2A · answer key

Unit 2A Practice Exam A Answer Key

Finish an honest attempt first, then compare one numbered response at a time and identify the first decision that changed your work.

Answer 1

Problem 1

$5$ .

Answer 2

Problem 2

Tangent $y-\frac12=-\frac14(x-2)$ ; normal $y-\frac12=4(x-2)$ .

Answer 3

Problem 3

$\frac{28}{3}x^{4/3}+10x^{-3}$ .

Answer 4

Problem 4

$e^x[(x^2+1)^4+8x(x^2+1)^3]$ .

Answer 5

Problem 5

$2\sin x\cos x/(1+\sin^2x)$ .

Answer 6

Problem 6

$\{10x\tan^4(1+x^2)\sec^2(1+x^2)(x^3+1)-3x^2\tan^5(1+x^2)\}/(x^3+1)^2$ .

Answer 7

Problem 7

$y'=-(2x+y)/(x+4y)$ .

Answer 8

Problem 8

$y-\pi/6=(x-1)/\sqrt3$ .

Answer 9

Problem 9

$-1/3$ .

Answer 10

Problem 10

$(x^2+1)^{e^x}e^x[\ln(x^2+1)+2x/(x^2+1)]$ .

Answer 11

Problem 11

$4x^3-9x^2+2$ , $12x^2-18x$ , $24x-18$ , $24$ .

Answer 12

Problem 12

Differentiability supplies a linear approximation and therefore continuity; $|x|$ at zero is continuous but not differentiable.

Answer 13

Problem 13

$R'(d)=1200/(d+12)^2$ ; $R'(12)=25/12$ response units per dose unit.

Answer 14

Problem 14

Product rule; chain rule in the exponential; chain rule and power rule in $(x+1)^3$ .

After the explanation

Use the section idea

Reading lens

Mixed practice tests recognition: the page title no longer tells you which rule to use.

Mental model

A dependable solution separates interpretation, rule selection, calculation, and verification.

Decision

Classify first, calculate second, and use answer reveals to diagnose the first incorrect decision.

Common trap

Reading the solution before making a complete attempt or treating every miss as mere algebra.

Check yourself

Can you explain why your method fits before comparing your final answer?

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