Show that e* ≤ 1/(1 − x) when x < 1. [Hint: Consider f(x) = (1 − x)e*.] -

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: 4. h(x) = x-T at X %3D 2. 5h(X) = x + x4-1 at X = %3D

A: Continuous function at x=a

Q: 6. Suppose t > 0. Consider the functions f(x) = e* and g(x) = xt. Show that ext for all x > 0, if…

A:

Q: For what value of e is the function defined below continuous on (-∞0,00)? C= 9. f(x) = [cx + 1,…

A:

Q: Q1 Let X1, .. ,X, f(r;0) = ()0 (1 – 0)2-, x = 0, 1,2. (i) Show that f(x:0) is a member of the…

A: It is an important part of statistics . It is widely used .

Q: Use mathematical induction to prove the following statement derivatives of the function f(x) = x¯¹…

A: We have to prove that the nth derivative of  where  is using mathematical induction

Q: 11. Consider the differential equation dy dt (a) Show that the constant function yı(t) = 0 is a…

A:

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: Jse the FOL Tableau technique to draw out the proof that the following formula is a valid rgument:…

A:

Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

A:

Q: 22. State True or False. Let f(x)=sin'(x) + log(x) then domain of f(x) is (-*, ). a) True b) False

A: To check whether the statement is true or not. The statement is Let f(x)=sin2x+logx then domain of…

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

A:

Q: Consider the function f defined by f(x) = x lxl for each * € R. How many times is f differentiable…

A: To determine the differentiability of the function  on  and , we need to analyze the derivative of…

Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

A:

Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

A:

Q: 87. Suppose that f and g are continuous functions such that, for all a, := | g(x)dx Give an…

A:

Q: Answer true or false. If f is not piecewise continuous on [0, ∞o>), then L{f(t)} will not exist.…

A:

Q: (153) (b) Let g(x) = 2***. Find g (x).

A:

Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

A:

Q: 1- f, 2x e dx

A: integration is given below

Q: Suppose that you know 3 18 O f(x) > 18 O f (8) – f (2) < 30 O f(1) is continuous on (-o, 00)

A: Using mean value theorem

Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

A:

Q: y 5 4 f(x) 3 g(x) 2 2 3 4 -1 1. 1.

A:

Q: Where is f(x) = e* continuous?

A:

Q: Use the cdf to determine E[X].

A: The E(X) using the cdf is calculated as E(X) = ∫(1 - F(x))dx Note : This formula can only be applied…