44. The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is GMr if r R 12 where M is the mass of Earth, R is its radius, and G is the gravitational constant. Is F a continuous function of r? 45. For what value of the constant c is the function f continuous on (-o, 0)? cx² + 2x if x < 2 f (x) = if x> 2 - CX

Q: 12. Consider x²y f(x, y) = g4 + y? for (x, y) (0,0) and zero otherwise. Is f continuous at (x, y) =…

A:

Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: 3. Suppose that f is a differentiable function of one variable. If we define u(x, y) = x² f(y + In…

A:

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

A:

Q: 2. (a) Suppose that f is a differentiable function such that |f'(x)| < c for every x. Show that for…

A: To Prove: a. If f is a differentiable function such that f'(x)≤c for every x.Then for any real…

Q: 4. Use the definition of derivative to compute the derivative of the following functions at x 1: a.…

A:

Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

A:

Q: true or false  if f(x) is continous at x=a, then f(x) is differentiable at x=a

A: False.    The given statement is not true in general.

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: 8. Given that f(r) is continuous at r = 0, is f(r) differentiable at z = 0? (If yes, find f(0) using…

A:

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x)…

A:

Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

A:

Q: Vx +1 for 0<x<3 (5-x for 3< x< 5 Let f be the function defined by f (x) = %3D (a) Is f continuous at…

A:

Q: Suppose g: IR - IR is a differentiable function with bounded derivative, Fix e> 0 , and define flx)…

A: to show f is one one we will show that for  x1 not equals to x2 , f(x1) is not f(x2)

Q: If G(x,y) is differentiable with respect to x and y then it is always possible to find the number…

A:

Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

A:

Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: Find given that z is a differentiable function of x and y, and xz + yz3 = 2 +x²ev

A:

Q: dy 6. If y is a differentiable function of x and r + 2y3 x² = 8y?, then find dr

A: This question is based on diffrentiation chain rule.

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

A:

Q: If we use trapezoidal rule for a function f(x) = x +2 1 - , then the approximate of J f(x)dx is…

A:

Q: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: If f(x) =0 at x=c then f has either a minimum or maximum at x=c. If a differentiable function f has…

A: To Determine: true or false                           1) if f'(x)=0 at x=c then f has either a…

Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 7 lim %3D х — 6 х—6 It…

A:

Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: 50 if x E Q 1 if x € R\ Q Let f(x)= Prove that y=f(x) is not continuous at any points a E IR.

A: Take p ∈ Q and let (xn) be a sequence of irrationals converging to p. Then f (p) = 1 but f (xn)→ 0…

Q: 16 8. If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

A: Given integral, ∫016f(x) dx =18

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: 46. The gravitational force exerted by the planet Earth on a unit mass at a distance r from the…

A:

Q: if z=0 ne function f(z)= )² if z+0 is differentiable at z= 0 LL

A:

Q: Suppose f is differentiable at a and f(a) + 0. (a) Prove |f| is differentiable at a by using that…

A:

Q: 3. Use the given graphs of the first and second derivative of a continuous function to answer the…

A: To find:- From given graph A. Set up a number line to represent where f'(x) is positive, zero, and…

Q: Suppose f(x) is a differentiable function. State the formula that determines the length of f(x) for…

A:

Q: Suppose g: IR →IR is a differentiable functionN with bounded derivative, Fix e> 0 , and defive fix)…

A: Consider the given information.

Q: 4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) =…

A: Given x2+3xy2+y3=9y2=-1

Q: 4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:…

A: prove of the above question is given below...

Q: The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center…

A: To find the continuity of F(r).

Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

A:

Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: 43 31) Describe all y=flx) which are defìned for all XEIR and satisfy continuoUs functions ə47…

A:

Q: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

A:

Q: 6) Answer the following True or False: Let  f(x) be a differentiable function, such that f(1)=−9…

A: The solution is given in the next step.

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.