Problem 4. Let's explore the infinite version of the above result true or not. For each natural number n, we define 1, fn (x) = { if |x| > 1/n n|æ|, if |æ| < 1/n. Explicitly compute g(x) = sup{fi(x), f2(x),-… , fn(x), … }. Is it continuous? ....

Q: 121. If f(x) = a", show that f(ax) = [f(x)]“. Problems 122 and 123 provide definitions for two other…

A: Given:  f(x) = axTo Show:  f(αx) = [f(x)]αProofFirst of all Replace x by αx in the f(x) , so we get…

Q: Suppose that ƒ′(x)&lt;= 1 for 1&lt;= x&lt;= 4. Show that ƒ(4) - ƒ(1)&lt;=3.

A: Show that:

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

A:

Q: . Let G(x)= x+3)2, if x ≤ -1; 2-x if 1<<1; Find all values of a where G is not continuous. , if x 1.

A:

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: 6. Suppose f(x)-<ɛ. Solve for|x-1 where f defined below. x 1 f(x) = 2 3

A:

Q: 7. Suppose f(x) = x³ – 27x + 1. Prove that f has exactly one root (zero) in the interval [0, 2].

A:

Q: 9. The interval for function (6-x)/4< (3x-4)/2 is

A: Find your answer below

Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: 6. Let f(x) be defined as follows: f(x) = {2f x is an integer (1 if x is not an integer Find each of…

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Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: . Solve the following a) Simplify f(x+h) - f(x) where f(x) = x^2-2x b) If f(x) = (x-2) (x^2-1),…

A: f(x)=x2-2x Now we find out f(x+h). Replace x with x+h f(x)=x2-2xf(x+h)=(x+h)2-2(x+h)=x2+2xh+h2-2x-2h…

Q: Write in point-slope form an equation of the line that passes 3 through (4, 8) and has slope m = 4 -

A:

Q: Example 15. Given the function { if x 1, ax + 1, f(x) = find the real constants a and b such that…

A:

Q: Let f (x) =12 x+4 %3D x+2 g (x) = x-1 x+2 Then (fg) (x) =

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 14. Consider the following function: if - 10 SIS0 3. h(r) = {15x - 3| if 0<<4 2r +1 if r24 What is…

A:

Q: 1. Determine and completely simplify f(x + h) – f(x) for f(x) = -7 Зх + 1

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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: 7. (a) List the condition(s) for a function to f(x) be continuous at the point x = c. (b) For the…

A: 7. The given function gx=2x+a+x+3x+2x&gt;-2x+4+bx≤-2. We have to find the values of a and b, such…

Q: 4. Show that the function log(1+ x) lies between functions x - and x for all x > 0. (Hint 2(1+ x)…

A: We will expand log(1+x) by Maclaurin's series. Let f(x) = log(1+x)

Q: ) State the i

A: The given function is kx=x2lnx2. To find the concavity of the function, take the second derivative.…