SURVEY OF CALCULUS I EXAM 1 QUESTIONS WITH VERIFIED ANSWERS

SURVEY OF CALCULUS I EXAM 1
QUESTIONS WITH VERIFIED ANSWERS
Discrete Compounding Growth - ANSWER-A(t)=P(1+r/m)^(mt)

Continuously Compounding Growth - ANSWER-A(t)Pe^(rt)

Log of 9 base 2 - ANSWER-2^x=9

Log of 3 base 1 - ANSWER-Log(3)/Log(1)

Doubling time - ANSWER-A(t)=P(1+r)^t

Half Life Function - ANSWER-A(t)=Pe^(rt)

Average Rate of Change - ANSWER-(f(x+h)-f(x))/h

Average Rate of Change over an interval - ANSWER-(f(b)-f(a))/(b-a)

Instantaneous Rate of Change - ANSWER-Limit as h approaches 0 (f(a+h)-f(a))/h

Secant line - ANSWER-passes through two points to find the average rate of change

Tangent Line - ANSWER-'perfect secant'; finds the exact rate of change at a given
point; denoted as f'(x)

Definition of a derivative - ANSWER-Limit as h approaches 0 (f(a+h)-f(a))/h

non-differentiable example - ANSWER-f(x)=|x|

the derivative of any function in the form of f(x)=c, where c is a constant, the derivative
will be - ANSWER-0

the derivative of a function in the form of f(x)=mx+b, where m and b are constants, is
given by - ANSWER-m
Linear Function - ANSWER-F(x)=mx+b

Quadratic Function - ANSWER-F(x)=ax^2+bx+c

Exponential Function - ANSWER-F(x)=ab^x

Logarithmic Function - ANSWER-F(x)=Logbx=y or b^y=x