Let f R R be continuous and let F be an antiderivative of/. If F) dr = 0 for some k > 1, then xf (x) dx Select one: O a. None of them O b. cannot be determined O c. is F(k)/k

Q: Let f: R R be defined as f(x) D 1 + x2 Let /= [- 1, 2), then f(1) = Select one: а. 1] b. (0, d. None…

A:

Q: [ 3 -dx 33 + 1 ]

A:

Q: Let F be a continuous function on [a, c} , where a < b< e, and F(z) dz = 6, F(2) dz = 9 A. Evaluate…

A:

Q: Let f(x) = 2x + x2 on [0,7]. Let p ={0,3,4,7}. Let a(x) = 2x2 on [0,7]. Give the numerical value of…

A:

Q: 5. Let f : R -→ R be defined by f(x) = 2x +9. Find a formula for f-1.

A: We need to find the inverse function of the real valued function f(x)=2x+9

Q: For what value of k is f(x) continuous at x=3? f(x) = (x-1)(x-3) 9-x² 3k, x=3 " x!= 3 (when x is not…

A: f(x)={(x−1)(x−3)9−x2,x!=3( when x is not equal to 3)3k,x=3

Q: Prove or disprove: If f is continuous, then S s) dx = [r(1-x) dx.

A:

Q: Evaluate fff f(x, y, z) dV for the specified and B: B f(x, y, z): Z | 8 2 ≤ x ≤ 6,0 ≤ y ≤ 6,

A: We have to find the value of the given expression according to the given information

Q: Given a function f: A → B and subsets X,Y C B, prove that f"(XNY) = f(X)nf-(Y).

A: He we will prove the given result.

Q: ) Let (x, y) €Rx R. Consider the following functions from R2 to R? r(x, y)) = (-y,x) and s(x, y) =…

A: Since you have asked for multiple parts, solving a) and b) , kindly post the remaining as a separate…

Q: Let f: [a, b] → R5 be defined by f(t) = (4t, 3 t², 2t*, e', 9). List F'(t)

A: Given that:

Q: 3c. Let 0 < a < 1 and ƒ : (a, 2) → R be given by ƒ (x) = ½. Show that ƒ is uniformly continuous.

A: Given: Let  and  be given by We have to show that  is uniformly continuous.

Q: 3. Let fn(x) = ¹+cos(nx), x € R. Find f(x) so that fn → ƒ pointwise on R, then check whether fn → f…

A:

Q: Show the following functions are continuous P• 18²R" such that fix,y) = (x₂ - y)

A: AS PER GUIDELINES WILL SOLVE ONLY FIRST QUESTION , PLEASE MENTION WHICH QUESTION TO BE SOLVED OR…

Q: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

A:

Q: Evaluate ſƒ ƒ(x, y, z)dS for f(x, y, z) = x and S is the cylinder x² + z² = 16 for 0 ≤ y ≤ 2.

A: Given: fx, y, z=x and S is the cylinder x2+z2=16 for 0≤y≤2. We have to evaluate ∫∫Sfx, y, zdS.

Q: Which of the following are functions from.16 ?the set of real numbers to itself fi = ((1,x): x E R)…

A: Given: The relations from set of real numbers to itself as f1=1,x : x∈Rf2=x3,x : x,y∈Rf3=x,x :…

Q: 6. Let S = {-1,0, 2, 4, 7}. Find f(S) (image of S under f) where f is from R to R for (a) f(a) = 1…

A: The

Q: Suppose f: R→IR is defined as follows: O Then f is continuous at 2 when b O 4 1 f(x) = 5 X, 3xb,…

A:

Q: 1. Determine whether f is a function from Z to R if а. f (n) %3D tn b. f(n) = Vn² + a %3| 1 с. f (n)…

A:

Q: Let f(x) =|x²-2x|, the ceiling function, and let S be the interval S =(1,3). Then f(S) is one of the…

A: fx=x2-2x S=(1, 3) fs=f1=12-21=1-2=-1 fs=f3=32-23=9-6=3   Given f(x) is a ceiling function  According…

Q: Suppose that f is a function which is integrable on the entire real line, and that a and b are real…

A:

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

A:

Q: f(x)=xmodx for all x  in R. Discuss the derivability of f(x) at x=0

A: Given:fx=xxwe have to find derivability of fx at x=0

Q: Let f(x)=1/x. Show that f is bounded from above on any interval (α,1), where α>0, but the function…

A:

Q: 6. Let f be function such that f(-a) = - f(2) for all If a %3D х. | f(2)dz = 5, then L2) +0)dz =…

A: With the help of definite integral property we solve this.

Q: Let f R R be defined as f(x)= Let /= (-00, 2), then f(1) = 1+ x? Select one: O a. (0, 1] b. (0, C.…

A: Evaluate the value of the function at each endpoint of the given interval to calculate f(I) .

Q: Let h : C N x N where C CZ given by h(m) = (m2 +1, m2 + 2). Choose all subsets C' such that h is an…

A: