-2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

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Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

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A: We know, ln(x) is defined for x&gt;0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

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A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

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A: You have to find the left and right hand limit for the given function.

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A: Use the given information.

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A:

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A: Here the given function  {1, sin 2x, cos 2x}

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A: Mean Value theorem

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Q: 6. Find the intervals on [0,2r)where f(0) = sin²(0) is concave upward/ concave downw %3D

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Q: 2. Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval then…

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Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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Q: Suppose f(x) = – 2x – cos r. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: Give an example of a (discontinuous) function that does not satisfy the conclusion of the IVT on…

A: Given: f(x)=sin1x    x≠00            x=0

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A: Explained below

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Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

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A: As per guideline we can solve only one question you can repost other questions in next question

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A: Take the help of derivative and try to prove the given statement in two cases.

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Q: A. Ifw=sin(x+bt)+cos(2x+ 2bt). Prove that =6? B. If f = x*y* + 2y sinx + x²lny then show that fxy =…

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Q: on [ 0, 2î] ,determine all velafive the Finction. .If f(x) = sin x t cos X extrema for

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Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

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Q: 1. Consider the function f defined on [0, ∞), 1 f(x) = sin- x + 0 x = 0

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Q: For the set of functions {sin(x), sin(2x), sin(3x), ...} = {sin(nx)}, n = 1,2,3, ... on the interval…

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Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

A: