16. Let gbe the composite function fo f, that is g(x)=(fof)(x)= f(f(x)). 4 21 -4-3-2 O 1 2 3 4 Use the graph of f to fill in the following table. (approximate where necessary).

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: What are the global max and min over the interval x E [0, 0) for the graph of f(x) f(x) = (X e)-3x

A:

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

A:

Q: For what value(s) of x is the function f(x) = } 2x + 4 (x² +x +1 if – 2 sxs1 if x>1 NOT continuous?

A:

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: 9. Find the value(s) of k that makes the function continuous over the given interval. fx) = {3x + 4,…

A: Solve the question number 9 as asked by the user

Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

A:

Q: ,15 15 ** Let f be a continuous function. If f(x)dx = 15 and f(x)dx = -8, then f(x)dx equals -5 В C…

A:

Q: 18. Suppose that f is a differentiable function such that f(g(x))= x, and f'(x)= |3D 1 1+(f(x))².…

A:

Q: 4 ,5 Let f(x) = 7x* In(x) f'(x)

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 10. Consider the following function. 1 x } x > Find the values of a and b that make f(x)…

A:

Q: The domain of the function g(t) = vt – 8 is O (8, 00) O [8, 0) O (-∞, –8) O R O R-{8}

A:

Q: To plot the function f(x) == %3D 2x over [0,5], we use fplot('exp^(-x) /2*x'[0,5)…

A: Since we are given with multiple number of questions and our guideline is solve the first question…

Q: 2. (i) Consider the following function of two choice variables Z-f(x,y) Write down the first order…

A:

Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

A:

Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: +1 Differentiate the function f (x) = In +1

A:

Q: 1) Sketch the graph of a function with the following conditions: V D = {x € R\x # 0,4, 5} f(x) 0…

A: We have condition at function.D = {x∈R|x≠0,4,5}f(x)<0, When x∈(-2,0)∪(2,4)f(x)>0, When…

Q: 35. Given that f(z) is a continuous even function, then A 0 B D

A:

Q: Suppose g is the function defined by picture where k and m are constants. If g is differentiable at…

A: Solution

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x<0   So,…

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x>3 now show that it is continuous at x=3 or not.…

Q: 1. Apply the Parseval's identity to the function f (x) = x, –n < x < n

A:

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: 2. Find the first 3 iterates of the function f(x) = 0.75x when xo = 5. %3D 5, 3.75, 2.8125 4.25,…

A: First iteration is x1 = .75*5 = 3.75... Second iteration is x2 = .75*3.75 = 2.8125... Third…

Q: 3. Define f(2) in a way that extends f(s) = -8 to be continuous at s = 2. s2 – 4

A:

Q: 10. Consider the function if a E Q -a? if x ¢ Q. f(x) = Prove that f'(0) = 0. %3D

A: Solution:Given  f(x)=x2if x∈Q-x2if x∉QTo prove f'(0)=0Formuladdx(xn)=nxn-1

Q: 18. Consider the function f (x) 5e2r. On what interval(s) is f (x) %3D increasing? On what…

A:

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: 9. If f(x) = ], ( 22 - 5t-3 ]dt, on what interval(s) 0, is f increasing, decreasing

A:

Q: Develop the Simpson's 1/3 rule to evaluate the value of a function. f(x) 1 between the yalue 1 and 5…

A: Hey, since there are multiple subpart posted, we will answer first question. If you want any…

Q: 14. Find the end behavior for f(x) = -x - 4 A. x- +o, f(x) +0 x--o, f(x) - +0 B. x- +o, f(x)-0 x-…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

A:

Q: 3 2. Compute f(x)dx for the following function. O if x 0 f(x) =

A:

Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

A:

Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

A: We need to find differentiation of f(x,y) with respect to x and y.

Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

A: