Consider the cases: (1) x = -4 (2) x = –2 (3) x = 0 (4) x = 2 (5) x = 4 Part (a) For each case, state whether or not f is continuous at the given point: (Enter "y" for yes, "n" for no.) (1) (2) (3) (4) (5) Part (b) For each case, determine if f is continuous from the right, or from the left, or neither. (Enter "r", "l", or "n", respectively below. In the case of continuity at a point from both sides, enter "b".) (1) (2) (3)

Q: Suppose f is differentiable on the set of real numbers R and a E R. Let F(x)= f(xª) and G(x) =…

A: F(x)=f(xα)F'(x)=f'(xα)ddx(xα) , [chain…

Q: Let f : Z+ → Z be the function defined by n – 10 (F(f(n+11)) otherwise if n > 100 f(n) What is the…

A: We will find f(99)

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f-1(E -…

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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: If f(z) <0 for all real numbers z then f is decreasing on (-o, 00) Select one: O a. False O b. True

A:

Q: Determine whether the following function is continuous at the given point x = 6: x2 8x + 12 - x + 6…

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Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: Determine which of the following functions are valid PSDS (i) wó + 30 +3 (ii) exp|- (@- 1)

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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: 3. Check for monotonicity for the following functions. TR = -20² + 14Q %3D TC = 20 + 10 100 AC = Q +…

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Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

Q: The function f (x) = 3x² –4x-3 is continuous everywhere.

A: Given,             f(x)=3x2-4x-3

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: Plot the poles and zeros of the following function: F(s) = 10(s+5)(s+3−j4)(s+3+j4)…

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Q: How many functions f: [6] to [4] have f(3)=2?

A: We have to find How many functions f: [6] to [4] have f(3)=2?

Q: Assume that f is a one-to-one function. (a) If f(1) = 8, find f −1(8). (b) If f −1(3) = −9, find…

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Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

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Q: How many radians are there in an angle of - 670°? Draw the angle?

A: Radians in an angle of - 670°  =   ? We know,      180o = π radian

Q: Determine whether the following function is continuous at the given point z- 3z+ 14z -5 f(2) 3z -1…

A: A function fx is continuous at x=a if limx→a-f(x) = limx→a+f(x) = f(a)  Given: fx=3x2+14x-53x-1…

Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: B. If f(x) = 3*, evaluate 1. f(2) 3. f (-) 2. f(-2) 4. f(0.4) 5. f(T)

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Q: Let a, b 0. Find f(100) (a) provided that x³ (a - bx)²* f(x) =

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Q: How many one-to-one functions f:[4] to [6] have 5 not in the rng(f)?

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Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

A: The given function is fx=11-x. Replace x by x+h and obtain that, fx+h=11-x+h. Obtain the difference…

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

A: