Reference no: EM132927743

Question 1 Find the limit of the function shown below at x = 2:

Question 2 Find the limit of the function shown below at x = 5:

Question 3 Evaluate lim_x→3 (x²-9)/x-3

Question 4 Evaluate lim_x→3 (x²+5x+1)

Question 5 The function shown below is continuous at x = 2.

Question 6 The function shown below is continuous at x = 3.

Question 7  Determine if the piecewise defined function below is continuous at the origin.

f(x) = x² + 5, x ≤ 0;  f(x) = 3x + 5, x > 0

Question 8 To what new value should f(2) be changed in f(x) in order to remove the discontinuity?

f(x) = 8x +-3, x ≠ 2;  f(x) = 4, x = 2 

Question 9 Derivative of a function is the rate of change of that function with respect to one or more variables.

Question 10 Find the derivative of the function f(x) = 6x - 9, and calculate f'(2).

Question 11 Find the derivative of 4x³ - 5x +6

Question 12 Find dy/dx if y(x) = 10 - 9x^1/3

Question 13 Find the derivative of s(t) = 3t² + 15t - 18

Question 14 Find the slope of the function f(x)= 2x² -4x+3 at x = -2.

Question 15 Suppose the demand curve for some product was given by D(p)=1/p, where D is the quantity of items produced, in thousands, at a price of p dollars.

Interpret what the derivative of D represents at p = $3.

Question 16 Let

f(x) = 4x³,

g(x) = 2x² +5x and

h(x) = 2f(x) - 4g(x)

Find

h'(2).

Question 17 For which values of x does

f(x)=6x^2+3x-1

has a tangent line of slope 15

Question 18 The cost, in thousands of dollars, for producing x thous and tablet cases is given by C(x)= -1/250.x² + x + 22

Find the value that best approximates the average cost when 10 thousand cases are produced.

Question 19 Find f'(x) if f(x) = (2x³+5x)²

Question 20 Consider the function

x    -1   2   3   4   5   6   7
F(x) 10 15 18 20 23 26 30

Find the average rate of change of the function from x=4 to x=6

Attachment:- MATH_Attempt.rar