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Calculus Exam #2 Study Guide question and answers graded A+ 2025/2026

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Calculus Exam #2 Study Guide question and answers graded A+ 2025/2026

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Calculus Exam #2 Study Guide

d/dx [e^x] - ANS-e^x

d/dx [-2/3 e^(-1/2x)] - ANS--2/3 e^(-1/2x) * (-1/2)

(lim as h approaches 0) [(f(x+h)-f(x))/h] - ANS-Msec (average velocity)

If differentiable - ANS-it's continuous.

If continuous - ANS-not necessarily differentiable.

sin'x - ANS-cosx

cos'x - ANS--sinx

tan'x - ANS-sec^(2) x

cot'x - ANS--csc^(2) x

sec'x - ANS-(secx)(tanx)

csc'x - ANS--(cscx)(cotx)

arcsic'x - ANS-1/sq root(1-x^2)

arccos'x - ANS--1/sq root(1-x^2)

arctan'x - ANS-1/(1+x^2)

Instantaneous Rate of Change - ANS-Slope of tangent line, lim as h approaches 0

When s(t) is increasing - ANS-v(t) is positive

S(t) is increasing - ANS-(t) is positive

V(t) is increasing - ANS-a(t) is positive

s(t) is CCU - ANS-v(t) is increasing & a(t) is positive

s(t) is CCD - ANS-v(t) is decreasing & a(t) is negative

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