1. Find constants a and b such that g(x) is continuous for all x, where if x<-1 g(x) = if if x³ ax + b (x²+2 -1

Q: Find value of the constant k if possible, that will make the function f(x) continuous at x = -3. [x²…

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Q: 9. Find the value of a so that the function g(x) is continuous at x = 0 where g(x) = { = 1 2xe3x 1…

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

A: topic - functions

Q: if 4x Suppose that g(x) = {ax + b xS-1 if - 1<x < 2 if x2 2 Find the value of a and b such that g(x)…

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Q: Find the value of m such that g(x) = {x+5 , if x ≤ m} and g(x) = {2x - 3 , if x > m} is continuous…

A: Function limit and continuity

Q: Find values of x, if any, at which the given function is not continuous. (a) f(x) (b) f(x) = |x³ -…

A: Find the x values where the function is not continuous.

Q: Initially 45 grams of radioactive substance was present. After 2 hours the mass had decreased by 6%.…

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Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

Q: 2 is > 2 of x, the

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Q: ii) f(x) = x*-1 %3D x²-1

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Q: True or False. The following function h(x) is continuous everywhere              h(x) =(x2-4/x+2…

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Q: For how many n = {1, 2, ..., 695} is n a multiple of one a multiple of one or more of 8, 3, or 7?

A: In the range of [1, 695] the number of numbers divisible by an integer k =  represents the floor…

Q: Find the value of a and b such that the function g(x) is continuous. x 3

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Q: What is the smallest integer a where f(x)=2x is always greater than g(x)=x2 for all x>a?

A: Given  : f(x) = 2x is always greater than g(x)=x2 for all x &gt; a  Implise that :  2x &gt; x2

Q: Q.1 Find all values of x, at which f is continuous and discontinuous. x²-9 f(x) = x-3

A: 1. Given function is, f(x)=x2-9x-3=(x+3)(x-3)(x-3)=x+3 As, the function is a polynomial function and…

Q: Find the values of a and b that make the following function continuous. 9x -C 9x if x 2 f(x) What…

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Q: Discuss the monotonicity of g (x), where g(x) = 2f + f(6-x) for all x e R. 2

A: Test for monotonicity:           let us consider a function is continuous on [a ,b] and it is…

Q: 4. Determine the constant m such that f(x) = {x2 + m, if x ≥ 3…

A: Given that: f(x)=x2+m, if x≥32x-m, if x&lt;3

Q: (b) Find values of x, if any at which f is not continuous (2x +3 xs 4 7+ x>4 f(x) = 16

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Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function