r kx + 5 for x< 2 Let f(x x – 1 for x > 2 Find the value of k for which f(x) is continuous at x-2. O A) -2 O B) -1 O C) 0 O D) 1 O E) 7

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: z+2 if x + -2 f(x) = if a = -2

A: f (x) x2-4x+2 if  x ≠ -2               k        if x = -2A function f (x) is continuous at a point…

Q: If the function f:R →R given by f(x) = x' + ax? + bx + 5sin? x is an increasing function, find the…

A:

Q: (x² + 2 , x² – xk – 3 , x 5 7. Find the value of K that makes the function f(x) = Continuous at x =…

A:

Q: X+4x+x-6 P+x-2 x+1,-2 Where is the function f(x)= x=-2 discontinuous? Oa. 1 Ob. -2 Oc. 1, -2 Od. The…

A:

Q: -X f(x)= cx+b ax² Where c= -2 Calculate a and b so the function is continuous for all R Show all…

A:

Q: Q1: - Find C that make the function f(x) continuous f(x) = {| x +3 Сх+ 6 x 2

A:

Q: for a 16 a. Determine the differentiability of the function at z = -2 and a = 8. Explain why the…

A: We are given with function d(x) for x=-2 , we use the first function  d(x)=|4-x2| When we graph the…

Q: A16: Function f is a continuous function and 2 f(x) dx = 6. Evaluate e (² xf (x²) -√√4 – x² dx.

A: The given integral value is .The aim is to find the integral..Formula used:.Note:Since you have…

Q: 9. For what value of the constants A and B is the function A√x+6-1 for Br² +2 f(x) = 2 Ar + B f…

A:

Q: (2ax + 4,x < 2 g(x) = 110, 7. Find the value of “a" if gx) is continuous for all 2 < x real numbers.

A: g(x)is  continues for all real numbers

Q: #9 Consider the following piecewise function: x-6x-7 f(x) = x+1 ,X=-1 What value of c will make f(x)…

A: Given:    Limit equation is given.

Q: 3x2 – 1 if x 1 Determine c and d so that f is continuous everywhere

A:

Q: Q4 Use an E-d argument to prove the function g(x) = x³ is continuous at E R. Hint: x³ x³ = (x −…

A:

Q: (c) Let k be a positive integer. Does there exist an entire function f such that f(z) = |2|k for all…

A:

Q: For what value of k will the function f be continuous on (-∞, ∞)? x² 2 f(x) = = x + 3 k if x # -3 if…

A:

Q: Let f(x) = and g(x) = 2х -1 Compute (f o g)(x) and determine the domain in x-2 interval notation.

A:

Q: f The domain where f(x) = 2(x + 1)(x-2)(x+3) is positive is Select one: a. x > 0 b. x2

A:

Q: Mark the correct answer. Let f be a strictly increasing and continuous function defined on the set…

A: Given   x 0 1 2 3 f(x) 3 9 16 22

Q: 15. Find the smallest possible real number a, such that the function is not continuous at exactly…

A:

Q: Ax - B xS-1. 5) Given a function h(x) = {2x² +3Ax+B, -11 a) Given that h(x) is continuous for any…

A: As per bartleby guidelines, for more than one question asked only one is  to be answered, kindly…

Q: Consider the following function: |3x 9x -18 1 -1 f(x) = -9x 18 9. %3D 2 12 0 1 a) What is the…

A:

Q: uestion 6: Suppose f: N N has the rule f(n) = 3n²-1. Determine whether f is 1-1.

A: