Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

Q: Let f(x) be a piecewise function defined by - 6x+ a if x - 3 What should be the values of a and b…

A: Continuity

Q: Show that f(x) = 2/x2 + 3x4 – 5x6 is an even function

A:

Q: Show that the function f (x) = (2x2 + 3)3/2 is decreasing for x 6 0 and increasing for x 7 0.

A: Given: f(x)=(2x2+3)32

Q: If f(x) = x2 - x/ x - 1 and g(x) = x Is it true that f=g?

A: given  f(x)=x2-xx-1g(x)=x

Q: f(x) = x* + x³ – 2x² For the above function state all intervals of x where f(x) is decreasing.

A: We know that if f'x&gt;0 at a specific value of x, then the function f(x) is decreasing at those…

Q: For the function f (x) = (*-2)* x+2 , find f-'(x).

A:

Q: Find the value of k which makes F(x) =(x+k)/(4k-1) if x&lt;=0 and F(x)= x^2+2x+k if x&gt;0 if…

A:

Q: For the function f(x) = 5x° -4x +2x + 3, findf "(x). Then find f"(0) and f"(4). f"(x) = Select the…

A: Double derivative

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: Differentiate the following function. y=x(x5 + 5) 3 Choose the correct setup below to differentiate…

A:

Q: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

A:

Q: find the interval where the function is increasing or decreasing  f(x) = 6/x-4

A: Function is not defined at x=4  there are two intervals where the function is defined   ( -∞,4 ) and…

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: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

A:

Q: (4x+7 (ii) If f(x) = { 14x²-1 Isxs2 2<154 determine whether the function f(x) is continuous…

A: In this question we have to check whether the given function is continuous throughout its domain or…

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

A:

Q: Choose all functions that are members of the same family. Oy=-x(x − 3)(x + 5) Oy=x³ + 2x² - 15x…

A: By simplifying each function, we can identify the members of same family.

Q: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: Let f(x) = x + 3 if x ≥ 5, 8 if x &lt; 5. Find f(12) - f(-12).

A:

Q: 7. Consider function below. What is the value of fl-5); f(0); 3) respectively? (4x+11, -10 Sx<-2 fx)…

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Q: b) Find the Constants "a" and "b" such that the following function is continuous for all real…

A: We have to properties of continuity first.

Q: x²x2 x - 3 ax + b -3 < x < 4 x³ + 4x x ≥ 4 Determine the values of the constants a and b that make…

A: The given function is,The function should be continuous so we can write,

Q: If F(x)=4-x and g(x) = 2x +3, find a value of such that F(x - 2) = g(2x). 40 22/10 0-2 O 0-1/3 O LO…

A: