#5. Prove that the fiz) = { is entive. function of defined by (e²-1-2)/2² 12/2 when z to when z=0

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: Prove that x² + ¹² +2111²2 = y 1112 where prime denotes differentiation w.r.t.s. 1 1+p¹² 4 p² o² + P

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Q: 5.16] Use the function f (x) = xe¯ ¯x² to find fave on [0,4] %3D

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Q: +¹²+z111² Prove that x12 where prime denotes differentiation w.rts. = 1 p² o² + 1+p¹² P

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Q: 6.3 Let g: R → R be a real-valued function defined by g(x) = x² + 2x - 1. Let A = (-2,3], and B =…

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

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Q: Use the function f(x) = 5x – 6 to compute and expand and simplify the following. a. f(-) = b. f(-6a)…

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Q: Prove that x² +¸µ111² +21112 where prime denotes differentiation w.r.t.s. = 1 o² + 1+p¹² P

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Q: Let f be a function defined on [15, 23]. Suppose for every x ≤ (15, 23) d da If f(16) = 44, find the…

A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

Q: 1. Consider the table of values for f given below: 3 f(x) 4 6. 5. Find the value of (a) ƒ-'(5), (b)…

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Q: u(1) = 2 and u' (1) -4. Find the tangent line to the curve и(х) cos(y) — 5eV — 3. at the point…

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Q: From algebraic form of function ez, prove that  |ez| = ex

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Q: Determine whether each of these functions from Z to Z is one-to-one. a) f(n)=n−1 b)  f(n)…

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Q: for t < -2 t+ 6 f(t) = for -1< t < 2 t2 -- t \3t - 2 for t 2 2

A: Given- ft=t2           for t&lt;-2t+6t2-t     for  -1&lt;t&lt;23t-2      for          t≥2   To Find-…

Q: Assume that a manufacturer has productivity function P(l, c) where I and c are the amounts of labor…

A: given  productivity function=p(l,c) l=amount of labor and  c=amount of capital utilized

Q: 11. Let f(x) be any function with the domain (-o, 0). a) Let e(x) = @)+f(-x), Verify that e(r) is an…

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Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

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Q: . There is a function f that's continuous at 0 and f(x) = f(2x) for all x's please show that f must…

A: Answer for sub question 1a: First step is to show fx=f2-nx for each integer n≥0. If n=0: fx=f2-0x…

Q: Let f be a function defined on [11, 25]. Suppose for every x = (11, 25) d. dx -f(x) = 0. If f(12) =…

A: Given query is to find the value o f(24).

Q: Suppose that u and v are functions, defined on their natural domains by the formuae u(x) = √x and…

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Q: In the set of functions C[0, 7] determine what of these two functions is convex (f"(x) > 0) and what…

A: In this question we have to find the which function is concave or convex.

Q: Q1) Check the continuity of the given function at the given c (or c's). 2-4z+3 if I+ 3 { (a) f(x) =…

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Q: This problem is about giving an example of a function from Z to Z that is onto, but not one-to-one.…

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