Calculus
Unit 2: Quotient Rule
f(x) = (5x2-6)/(2x+3)
The derivative of the function solved using the quotient rule:
What is fl(x) = (10x2+30x-12)/(2x+3)2?
Unit 2: Derivatives
The derivative of the following function.
f(x) = 3x8-4x2+2x+37
What is fl(x) = 24x7-8x+2?
Unit 1: Squeeze Theorem
Let g and h be the functions defined by g(x) = x2+2x-4 and h(x) = -x3-5x-22. If f is a function that satisfies g(x)<f(x)≤h(x) for all x... the limit f(x) as x approaches -2.
What is -4?
Unit 1: Estimating Limit Values from Tables
*** Calculator activated (See table on whiteboard)
The function f is continuous and increasing for x≥3. The table gives values of f at selected values of x. The approximate the value of lim 2(cos(f(x)))2 as x approaches 4 (to the nearest thousandth).
What is 1.137?
Unit 3: Chain Rule
The derivative of the following function solved using the chain rule.
y=e√4-sinx
What is dy/dx = (-cos(x)e√4-sin(x))/(2√4-sin(x))?
Unit 3: Implicit Differentiation
dy/dx of the following.
lny4+cos6(X)=3-y
What is (6cosxsinx)/((4/y)+1)?
Unit 6: Riemann Sums
Let z(t) represent the rate of changeof the population of a town over a 10 year period where z is a differentiable increasing function of t. The table shows the population change in people recorded at selected times.
(See table on white board)
Use the data from the table and a right riemann sum with four subintervals to approximate the area under the curve.
How many are 48,308 people?
Unit 6: Integration Using Substitution
The indefinite integral of ∫e1 ((lnx)/x)dx.
What is .5 or 1/2?
The general solution of dy/dx = 2x3y solved using separation.
What is y = Ce3x^2?
A bird is born 5 inches tall; and grows to 9 inches 4 months later. Its height increases proportionally to its height. Establish a differential equation and find the birds height when it is 6 months old.
**Calculator active.
What is h(6) = 12.07476707 inches?