Which of the following is the correct limit defihition for the derivative of g(x) = + 4? Select the correct answer below: (x+h) +4 - ( +4) lim (x+h +4- ( +4 lim (x+h) +4- (+4 lim Ha -(+4) +4

Evaluate Function  g(3,4) when g(x,y)=x-6y/x^2+y^2 a. -25/21 b. -5/21 c. -21/25 d. -21/5

Consider the function f(x)=x/x^2+12x+32. Determine the intervals on which f is increasing and decreasing. Your answer should either be a single interval, such as "(0,1)", a comma separated list of intervals, such as "(-inf, 2), (3,4)" , or the word "none".

Find the difference quotient for each of the following functions and reduce to lowest terms A. f(x)=2x^2-3x+7 B. f(x)= 2/4-5x

Please classify the Type of Discontinuity of the following functions:

Determine the value(s) of x for which the following function is discontinuous. Identify the type of discontinuity. Justify your response.  f(x) = 2x^2+3x−2/ x+2

(x)gm Apply the limit definition to find the derivative of the function, f(x)=2x -5x+9. Not the short cut version. f

Consider the function f and its derivatives below. f'(x) = -2(2³-32) (³+64)² 6x²(³-128) (3+64)3 f"(x) = f(x) = 3 +64 Fill in the table below. For answers that require intervals, use interval notation and write your answer as a comma-separated list of intervals that are as inclusive as possible. Write "NONE" as your answer, if appropriate. Your answers must be exact or accurate to two decimal places. 2 1.26 38=2 4 1.59 16 2.51 √32 3.17 equations of vertical asymptote(s) of f: equations of horizontal asymptote(s) of f: f is decreasing on: f is increasing on: z-coordinate(s) of each local minimum of f: z-coordinate(s) of each local maximum of f: f is concave down on: f is concave up on: 01 x-coordinate(s) of each inflection point of f: √64=4 128 5.04 Sin den Ja

Use the definition of the derivative (don't be tempted to take shortcuts!) to find the derivative of the function f(x) = 5 – 5x + 7x?. Then state the domain of the function and the domain of the derivative. Note: When entering interval notation in WeBWorK, use I for o, -I for –∞, and U for the union symbol. If the set is empty, enter "{}" without the quotation marks. f'(x) = Domain of f(x) = Domain of f'(x) =

Which of the following is a point on the graph of the function 5 - 3x f(x) = 4. (-5,5) (2,-1) (-3, 14)