CALCULUS OF THE LIFE SCIENCES
EXAM QUESTIONS WITH COMPLETE
ANSWERS
What is the derivative?
f(x) = ^3√x^2 - ANSWER-- x^2/3
or
- 2/3x^-1/2 = 2/3 ^2√x
What is the derivative?
f(x) = 3/4^4 - ANSWER-12x^-5
What is the difference quotient? - ANSWER-f(x+h)-(f(x)
_______________
h
Lim f(x) = 4
x > 2 - ANSWER-As x approaches 2, y is very close to 4
Lim f(x) = 2
x > 2 - ANSWER-As x approaches 2, y is either undef. or = to 4
Does the limit exist?
Lim f(x) = 4
x > 2 - ANSWER-
Lim x^2 - 9
________
x > 3 x - 3 - ANSWER-Step 1: (x-3)(x+3)
_____________
x-3
Step 2: (cross out)(x+3)
______________________
cross out
Step 3: x+3
Step 4: 3
EXAM QUESTIONS WITH COMPLETE
ANSWERS
What is the derivative?
f(x) = ^3√x^2 - ANSWER-- x^2/3
or
- 2/3x^-1/2 = 2/3 ^2√x
What is the derivative?
f(x) = 3/4^4 - ANSWER-12x^-5
What is the difference quotient? - ANSWER-f(x+h)-(f(x)
_______________
h
Lim f(x) = 4
x > 2 - ANSWER-As x approaches 2, y is very close to 4
Lim f(x) = 2
x > 2 - ANSWER-As x approaches 2, y is either undef. or = to 4
Does the limit exist?
Lim f(x) = 4
x > 2 - ANSWER-
Lim x^2 - 9
________
x > 3 x - 3 - ANSWER-Step 1: (x-3)(x+3)
_____________
x-3
Step 2: (cross out)(x+3)
______________________
cross out
Step 3: x+3
Step 4: 3
