Ql:a) check the continuity of f(x) at x = 1,2, 3 and 4 Osx s1 2-x 2 f(x) ={3 2x - 2 10-2x x= 2 2

Q: 15. Discuss the continuity of the function f (x) = x²-4. x-2

A: To find the continuity of function we need to find the domain of function

Q: Let f(x) = (x-9)7 – 8, determine f¯¹(x). - ƒ¯¹(x) =

A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: The function f: RR defined by f(x) = 5x3 + 3x2-x + 7 is O(x). True False

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Q: f:R - R S6 – x2 x 2 1 x < 1 fx 4x + 1 x=1, x= -1-

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Q: Consider the function f(x) the difference quotient = 7 x²+1/ 3 4 -X-2. Compute f(xo+h)-f(xo) h

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Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

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Q: (x? + 3x f(x) = - 6x if xs-2 if x>-2 A) Check the continuity of the function f(x) at x = -2 %3D

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Q: Analyze the continuity of the following function f(x) = 4x + 10      0 ≤ x ≤ 15 at the point x=8

A: The answer is given below:

Q: 5 - x, -1 sx 2 r - 1, 2 <xs 3 Discuss the continuity of g(x) = %3D

A:

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…

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Q: Identify the real number at which it is not continuous of the given function

A: To find: The real number where the function is not continuous. Given: The function is fx=xx2-4x+4.…

Q: (x2 + 3x f(x) = 3 – 6x if x -2 Check the continuity of the function f(x) at x = -2

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Q: x + Vx? -1 f (x) = X

A: Consider the given function, fx=x+x2-1x the domain of the function is the set of all possible real…

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

A:

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Let f (x) = 2x3 - 3x2 - 36x + 14. Also, let a = 0 and b = 1. (a) Show that the function f is…

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Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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Q: (B) Test the continuity of the following function: (3 Marks) (5x +3 f(x) = }2x2 +5 - 5x + 3 ;x< 2 ;…

A: F(x) is not continuous at x equals 2 and 4, and continuous at all other real numbers.

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: 5 - x, -1sxS 2 r² – 1, 2<x < 3 Discuss the continuity of g(x)

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Q: f(x) = x+1 x-3

A: Given:  fx=x+1x-3To prove: f(x) is 1-1 we know that, If f(x1) = f(x2) then x1 = x2 therefore f(x) is…

Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: Study the continuity of the following functions and show the process of how you tell if it is…

A: Here is the full solution for both Parts: To study the continuity of the functions provided in the…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.