1. Let f (-1,1) R, f(x) = (1+x³3)-3. Compute g': (0,1) → R where : (a) g(x) = få ƒ. 0 (b) g(x) = [ x f. f.

Q: : Consider the following function. H(x, y) = 10 In(x2+ 3y³) (a) Find f(2, 3). (b) Find fy(2. 3) .…

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Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: Find the Green's function G" + k²G = 8(x − s), Gʻ(0, s) = 0, G′(0,π) = 0 -

A: To find the Green's function G(x,s) for the given differential equation G′′+k2G=δ(x−s), subject to…

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: For any prime p, establish each of the assertions below: (a) t(p!) = 2t((p – 1)!). (b) o(p!) = (p +…

A: Tau function : It is  the number of divisors function, denoted by τ  τ is a multiplicative…

Q: The function f is defined by ƒ (x) = -2x³ – x – 5 and f(-1) = -2. If g(x) = f¯1(x), what is the…

A: Given fx=-2x3-x-5f-1=-2Therefore, f-1-2=-1Differentiate with xf'(x)=-6x2-1f'-1=-7

Q: 67. Consider linearly independent vectors v1, v2, ..., vp a subspace V of R" and vectors w1, w2,…

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Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Give two distinct linear functions ƒ and g that satisfy ƒ'(x) = g'(x); that is, the lines have equal…

A: It is given that fx and gx two distinct function.

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (1) and s'(4). y…

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Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: Let y=y(x)=2(√x)⋅f(x) and suppose f(4)=2, f′(4)=-2, find y'(4)

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Q: Suppose the slope of the curve y = f¯¹ (x) at the point (4,7) is . Find ƒ'(7). [B] 4 [A] 1 [C] 5 [D]…

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Q: 7. Let f(x) = (x² + 7x) e. Calculate f"(1), the sec- ond derivative of f at x = 1. (a) 2e (b) 17e…

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