Let f be in R[a, b]. Prove that -- f is in R[a, b] and ∫a b -- f(x)dx = -- ∫ab f(x)dx.

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = tan x, a = π

A: The linearization of a function f(x) at x = a is, Now differentiating  given function with respect…

Q: If f is continuous on A) True B False on [a,b], then Sº [ f(x a xf(x) dx = x f(x) dx

A: It will solve by part method integration  ∫u v dx = u∫v dx −∫u' (∫v dx) dx u is the function u(x) v…

Q: Let f be a continuous function such that f(x) dx: = -1 and f(x) dx = = 9. %3D 2 2 | f(x) dæ? What is…

A:

Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

A:

Q: Let f(x, y, z) = ln () Vxy – sin (cos (zy)) , evaluate ху %3D дх ду

A:

Q: Define f(x) = x if x is rational and f(x) = 0 if x is irrational. Compute So f dx and ſ f dx. Is f…

A:

Q: 2. Let f and g be integrable functions such that f(x) dx = 6 and g(x) dx = –2. Using the Linearity…

A:

Q: | (sec 4x – 1)dx

A:

Q: KB is ∀xy F(x, y). Prove using resolution-refutation that ∀xy F(y, x).

A: Solution: First, we convert clauses to CNF : (1) ∀xy Fx,y from KB (2) ∀x Fx,Ax (3) Fx,Ax CNF

Q: Let F(x) –3 cos(ť²) dt. Use the Fundamental Theorem of Calculus to find F'(x). F'(z) =

A: Given: F(x)=∫x−1(−3cos(t2))dtF'(x)=ddx∫x−1(−3cos(t2))dt=?

Q: If f is bounded and integrable on [a, b] sch that | f(x) | 0). 9.

A:

Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find a potential function for F or determine that F is not conservative.〈F = z, 1, x〉

A: F is conservative when curl F = 0 Given that f=(z, 1, x)=zi+j+xk Now evaluate curl F, curl F = ∇ × F…

Q: f (x) dx f (x) dx. a

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing you the…

Q: Let f be a continuous function such that | f(x) dx = -10 and | f(x) dx = 9. What is the value of…

A: Given: Let f be a continuous function such that ∫52fxdx=-10 and∫-25fxdx=9. To Find: What is the…

Q: Prove that the function f : R? → R, f(x, y) = sin(/x² +|sin y|) is uniformly continuous on R?.

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

Q: Iff is continuous on [a,b], then rtf(x) dx = π f(x) dx 1 A True B) False

A:

Q: Let f be continuous on the interval [a,∞). Show that if the improper integral ∫∞a ∣f(x)∣ dx…

A: If f  is a continuous function on the interval [a, ∞). If  ∫a∞f(x)dx converges, Then, we use…

Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

A:

Q: The tangent function f (x) = tan x is integrable from 0 to T. O True O False

A:

Q: For what value of a is

A: Given           f(x)=x2-1    ,  x<32ax       ,   x≥3

Q: b)S godx=? glx)dx=? ラg

A: To find the integrations

Q: Evaluate the integral f 2x (x2 + 7)° dx using the substitution u = x2 + 7. 2.x (x² + 7)° dx +C

A:

Q: Let F(x, y, z) = z* +x+y sin x +x In z 0, where z =f(x, y), then at (0,0,1) and %3D are equal to:

A: Given,          Fx,y,z=z4+x+ysinx+xlnz=0 , where z=fx,y

Q: 5 dx 8x (x+1)? 1

A: First evaluate indefinate integral

Q: What is f'(x) given the integral function f(x) = cos Tud u? O f(x) = -2x cos( T) %3D O f(x) = -2x…

A: The detailed solution is given below Thank you

Q: Suppose f is Reimann integrable on [a,b]. If f (x)< 0 for all x E [a, b], then S f(x)dx

A:

Q: Suppose that f and g are integrable and that -1 f(x) dx = 5 h(x) dx = 4 7, dx = %3D Use the rules to…

A:

Q: Show that (d/dz)ž does not exist anywhere, i.e., f (z) =z is non-analytic anywhere.

A:

Q: Let f(x)= In (V=) x - 5 Choose the interval(s) for the domain of f. Enter the endpoint values in the…

A: We have to find the domain

Q: Suppose f> 0 is integrable on [a, b], continuous at xo € [a, b], and f(xo) > 0. Prove that f>0.

A: Given f≥0 is integral on a,b continuous at x0∈a,b and fx0&gt;0

Q: Let f(x+ y) = f(x).s) Vx, ye R.Prove that f is derivable on R iff it is derivable at one point of R.

A: If the given function is continuous at x=a then it is continuous at x=b.

Q: Then, write a function f(z) such that a) it is analytic in C except its isolated singular points,…

A:

Q: Suppose that f and g are integrable and that f (x) dx : :-1 | f(x). h(x) dx = 4 Odx = 5 Use the…

A:

Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: Let f(z) = sin(z"). %3D f'(x) = 3x cos ) COS f'(4) =| 0

A: The given function is  f(x) = sin(x3)  We have to find the value of  f'(4) .

Q: Let u be a differentiable function of x. Use the fact that ∣u∣ = √u2 to prove that

A: Given that - u = u2          ............(1)To prove - ddxu = u'uuProof - Difefrentiating equation…

Q: Let f be the function defined by SI+x, when 0<x<!, }<x<1 0, when x=1. f(x)=: Show that fis…

A: We know that  A bounded function f which has only a finite number of points of discontinuity in…

Q: If f is continuous on [a,b], then f(x)dx= π + A) True B) False f(x) dx

A: Given that f is continuous on a,b. ∫abπ fx dx = π ∫abfx dx Say that the statement is true or false.…

Q: Let f(x) = (cosh x)² be defined on (0, 0), find %3D d 1/2) . dy

A:

Q: Prove that the function f(z) = sin(x)cosh(y) + i cos(x)sinh(y) is entire.

A:

Q: If f is integrable on [a,b], show by example that F (t) = | f (x) dx is continuous but need not to…

A: We need to show by an example that if f is integrable on [a, b], then F(t) (as defined in the…

Q: What is the continuous extension of f(x) = at point x-1. x -1 x2-1' %3D x +x-2 find dy dx

A:

Q: Let f be a continuous function such that f (x) dx = -4 and 1 f(x) dx = –14. What is the value of 2…

A: As we know that;  The properties of the definite integral; 1). ∫abfxdx=-∫bafxdx…

Q: Let f be the function defined by fx)=1+x, when 0<x<}, }<x<1 0, when x . Show that fis integrable…

A: We know that  A bounded function f which has only a finite number of points of discontinuity in…

Q: If X is a continuous RV, prove that E(X) = [1- F(x)] dx – F(x) dx. %3D

A:

Q: Find the Wronskian of the set of functions {e*,e® sin(x)}.

A:

Q: Let f be the function from R to R with f (x) = x2. Is f invertible?

A:

Q: Assume that ƒ is differentiable on a&lt;=x&lt;=b and that ƒ(b)&lt;ƒ(a). Show that ƒ′ is negative at…

A: Given,