Q1. For each of the following, determine which of these choices is correct. (A) The evaluation of f V1+lnx is 3 (1+lnx)* + c (i) (ii) 4 (1+lnx)* +c 3 (iii) None of these (x²-1)dx (B) The evaluation of S -dx is (x*+3x2 +1)[tan-1() In tan-| +c -in [tan"|+c (i) (ii) (iii) None of these (C) The evaluation of the integral J cos³e de is (i) +In 3 3 (ii) +In 3 (iii) None of these

Q: Evaluate f x'V 1+4x² dx.

A: Consider the definite integral ∫01x21+4x2 dx to evaluate this, first evaluate the indefinite…

Q: y y (x₁, y₁) f'(x₁) = ? ******** y = f(x) = ? (x₁, Yi) X y = f(x) ४ ✓ Choose... Ordinary…

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Q: 19. (2 points) Let ƒ be an even function such that = 216 and f(x) dx = 240. Evaluate (2 - 2)5(#) dz.…

A: The given data is : ∫03fxdx=216  and  ∫-23fxdx=240 To find: ∫-22x-2fxdx…

Q: Differentiate

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Q: X x + 2 A1. The functions f and g are defined by f(x) (a) Calculate f'(x) and g'(x). d (b) Calculate…

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Q: Integrate S (2x+1) Staz+X+4) dx

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Q: Approximate f(3) centered at 0 of f(x) = 2x³ + 3x² + x - 1. %3D

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Q: 3x+1 Evaluate f'(-1) given that f(x) = %3D 2x+1

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Q: EVALUATE Зд - 2 (c) dr x2-6x+ 8 EVALUATE sin-1x dx V1-x2 (d)

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Q: Differentiate. f(x) = In (4x+5)(x+8)5 (1-4X)6

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Q: Find the following using the table below. X 1 2 3 4 3 4 f(x) 2 1 f'(x) 2 4 3 1 g(x) 2 4 3 1 g'(x) 2…

A: 1) given function h(x)=f(x).g(x)Derivative w.r.t 'x' by using the product ruleformula of the product…

Q: x +1 dx x(x² + 4)' (f) | #(2² + 4) ع و ش

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Q: Provide the table of signs for both f' and ff'.

A: Given function is fx = x+334x-12 = x4 +12x-1+16x-12 +114. Also, given that f'x = x-9x+324x-13    and…

Q: Evaluate (*(x-2) (х-1)3

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Q: Find an anti-derivative F(x) of f(x) = 7x³ – 6x² –- 1 satisfying that 7 F(1) = 4

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Q: 2) Find all relative extrema of ƒ(x)= x* – 4x³

A: Answer

Q: Find ao of the function f(x) =(T - x)2 |3D | O 5 T^2/12 5 π^2/6 O T^2/12 TT^2/6

A: Fourier coefficient of the function

Q: Suppose f(x) = Evaluate: f(x) dx (A - In (2) (B) 4 3 16 (D) In (2)

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: (x+3)³ 4(х — 1)2 12 16 f (x) Consider the function 11 + 4. Note that %3D 4 x - 1 (x – 1)2 (x – 9)(x…

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Q: Let f(x) ƒ'(x) = ƒ'(3) = = √2x² + 4x + 3

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.