2²h Q2: Show that + əs² = * ər 2²h at=0 if h(s, t) = ln(√s² + t²) 8ºf (x² + y)² 8ª²f → (x² + y²) (x²+)

Q: D. Differentiate the following. a. f(x) = 4x³ – 5x² + x + 8 b. g(x) = x" -* -*+* + vZ c. h(x) = v9x°…

A: (a) To find: The derivative of fx=4x5-5x3+x+8. Formula used: Power rule of derivative: xn'=n·xn-1…

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(h(2))) B.…

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Q: Sketch c(t) = (t^2 − 4t, 9 − t^2) for −4 ≤ t ≤ 10

A: Given c(t)=(t2-4t, 9-t2)    ; -4≤t≤10

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

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Q: Determine a value for m so that h (x) = -1/3 x^3 + nx^2 + 8x – 15 has an inflection point at  x = –…

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Q: Find f'(x) for each of the following:< Ax) = 3x³ – 2x +4 b Ах) — 3(х + 2)? -2е a 8x* – 3x Ax) = Ax)…

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Q: s the following statement true or false? f(x)=e^x−9  is not a polynomial. a) True b) False

A: Given:                f(x)=ex-9   To determine:                               f(x) is a polynomial…

Q: Let f(x) = v9x+ 8 and g(x) = x+9 be functions from R to R. Find the following. a) (f • g)(x) = %3D…

A: We are given f(x)=9x+8 and g(x)=x+9 and we need to find different composition of the function.

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: (b) (x*y2,1/3(xy) -1/3 X + 0, y # 0

A: We will simplify the expressions by writing the exponents with equating the bases.

Q: f(x) = Ax , g(x) = Bx^2 Find A and B if (f o g) (1) = 11

A: This is a simple question based on composition of functions which could be solved with the basic…

Q: a) f(x) = {(3, –4), (2, 1), (–9,–3)} |

A: We have to find domain and range

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

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Q: Find the differentiate

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Q: 1. Differentiate. Do not simplify. I b) g(x) = (7x3 – 3x² + x)(1+ 4x²) a) y = Vx4 -5x+1 d) g(x) =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: CLX 5) Let f(x)=√√x³- 4x + 1, f(3) = 4, find (f¹)'(4).

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Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

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Q: find

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Q: Find the derivative. fx) = (4x - 4) + 20x - 20 O Pid - 6x1/2. 4x 1/2, 20 O fid - áx1/2. 2x 1/2, 20 O…

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Q: Let a, b 0. Find f(100) (a) provided that x³ (a - bx)²* f(x) =

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Q: Pls help ASAP

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Q: 7- Differentiate Y= f(g(x4)) h³(√x)

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Q: 2х f(x) = ,x 1

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Q: る(4xナx)(10x2+x2-2

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Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: Let y = || = y'"' = = x + 7 X X Hint: Try to do this without using the quotient rule.

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Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

A:

Q: Vipul

A: The objective of the question is to find the probability density function of the random variable Z,…

Q: 2. Given that f is a differentiable function with f'(3) = -5, find g'(1) where g(x) = f(4x-x²)

A: The given function is,