Find a function f and a real number a such that :| f(t) dt = x tan-r. + 4

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4

A: According to question, Local linear approximation,lx = x2 +π4-12,         .......1Given Function,fx…

Q: Use the Chain Rule to find dz/dt if z= (x+y)e^x, x= 2− t^2, and y=t

A: Given that: z=(x+y)ex,      x=2-t2 and y=t

Q: If f(æ) = S Tm dt for x > 1, 1 | In t find f'(2).

A: Please refer the attached image for complete solution.

Q: Solve the initial-value problem for a as a function of t . dx (t² – 6t + 5). = 1, (t > 5, x(8) = 0)…

A:

Q: If g(x) J.J S. 1 -dt , find g'(2).

A:

Q: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: Let f(x) be a function given by f(x)= { (a) Prove whether f(x) is a Dirichlet function. = for Tx<0,…

A:

Q: 3 62 what is 13 | f(t) dt? f(x)dx = 3 6.

A:

Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: psin(rx) (b) Let g(æ) 1 and f(x) g(t) dt. Find f'(2). x4 + 1

A: We have to use derivative under the functional limit formulae first then put x=2.

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: Given:         8y3+x2=1dxdt=2x=3y=-1 Differentiate 8y3+x2=1 with respect to t,…

Q: If f(x) • cos ( z ) t'dt then f'(x) =

A: We can find the answer as below

Q: Find F '(x). F(x) = 4 tan(t) dt J- F '(x) =

A:

Q: assume that x and y are both functions of t and find the required values of dy/dt and dx/dt.…

A: Given y = sqrt x =x(1) Given x = 9 and dxdt= 2∴dydt= 12x .dxdt by chain rule⇒dydt= 129 .(2) = 19…

Q: e + f(t) dt = x*e*

A: As we know that; The fundamental theorem of the calculus is: ddt∫atfxdx=ft Where 'a' is an arbitrary…

Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

A:

Q: Find the function f(x) and all values of c such that

A: To find the function f(x) and all values of c such that∫cxf(t)dt=x2+x-2

Q: e If F(x) = | e dt, find F(1) and F'(x). ez

A:

Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2

A: Using leibniz rule  Explanation is given below....

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

A:

Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: Find a value of x such that

A:

Q: If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

A: If Fx=∫π3xt2+1sintdt, then evaluate the value of F'x.

Q: Show that f(x) is one-to-one and find ( f −1 )′(0).

A:

Q: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

A:

Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

A:

Q: Suppose X and Y have the joint pdf f (x, y) = c(1.57 – x – y), x+y 0, y > 0 - a) Find the value of…

A: Introduction: The joint density function of two random variables X and Y is given below: (a). Find…

Q: 6. let h be the function defines by h(x) = 2e***dt, Find h'(2) %3D

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: Given that F(x) = Vt? + 1 dt calculate F"(x).

A: Given that Fx=∫x0t2+1dt                                     ……(1) We have to find F''x. First we…

Q: Show that f(t) dt ) dx (x - a)f(x) dx.

A: To prove: ∫ab∫xbftdtdx=∫abx-afxdx

Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

A:

Q: Let f(x) = S V4 – t? dt. - (a) Compute f'(x) (b) What is the domain of f(x)?

A:

Q: Solve the initial-value problem for x as a function of t. dx (t – 12t + 35) dt 1, (t > 7, x(9) = 0)…

A: The given initial value problem is as below.

Q: Calculate dy/dt using the given information. xy+x=12; dx/dt=-3, x=2, y=5

A: To calculate (d y)/(d t). find the slope of tangent line of the given curve by using implicit…

Q: Let g(x) = [" sin(t²) dt- Calculate g' (3).

A:

Q: a) If d'r = 3, when t = 0 we have dt? dx 0 and x=0, what is x as a function of dt t?

A:

Q: cos(x) If f(x) = ["(@) "g(x) V1 + t3 dt, where g(x) = S [1 + sin(t²)]dt, find f'(;). 1 %3D

A:

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: f(t) dt t sin(rx), -? What is the value of f(5) if

A:

Q: df Let f (x) = esinx and x(t) = t2 . Calculate a t = VT. dt %D

A: The given functions are fx=esin x  and  xt=t2. The given value of t is t=π.

Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: f(æ) = / t2 – 9 dt 1+ cos? (t) At what value of x does the local max of f(x) occur?

A: Given: For the local maximum value of f(x), we must have f'(x) = 0. Here,…