40! p(X =x) = „ х!(40 — х)! (p)*(4)"* 40-x , х %3D0,1,..,40 : A V(x) q 0.1 Lae О 2.5 1.4 О 3.6

Q: n(n+1)(n+2) E = =1i(i + 1) i=1 3

A: We will prove the given statement by using the principle of mathematical induction in which we show…

Q: The time T of oscillation of a simple T Vg pendulum of length | is given by T = 2π Find percentage…

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Q: to set Up Tutoring: (888) 1. Take the derivative of y = (7+x)(7+z) select Derivative does not exist…

A: The objective is to find the derivative of y=(7+x)(7+x)2 .

Q: '7 '7 If [ f(x) dx = 10 and ² fix 5 X f(x) dx = 3.2, find *5 [² f(x) dx.

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Q: If h'(3) -1 and h'(1) = 5, then |h"(z)dr = %3D %3D (A) -6 (B) 4 (C) 5 (D) 6 (E) 9

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Q: If Va? – 25 () then f'(6) = f(x) = x cosh

A: Given:

Q: 7. 7. '5 If f(x) dx = 8 and 1 f(x) dx 5 3.3, find f(x) dx. %3D

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Q: AF f(1) = 6 glD=5 h(1) = 3 f'(5)=-7 g'(5) = -11 (5) = 15 f" (-11) -2 - g" (-11) = 3 f(1) = 4 g(1) =…

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Q: If f(x) = 5 - 2? find: 8+ x2 f'(z) = %3D

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Q: (11) (g(h(x))) and h(1) = 5, g(5) = 3, h' (1) = 4, g' (5) = 10 and f'(3) = 8, then r' (1) = If r(x)…

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Q: On the interval [-5,5] (2²³, 2) = -(/ dx = da) ² =

A: Inner product of two functions

Q: '5 7 f(x) dx = 11, evaluate 15 Given f(x) dx = 19 and 7 (a) f(x) dx.

A: Given : ∫05fxdx = 19∫57fxdx = 11

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: 6. The solution of the equation 3(1 + 401) mately) (a) None. (b) 69.3 (c) 0.693 (d) 6.93 = 27 is…

A: 6. Given:3(1+4e0.1x)=27Solving for x, we have:33(1+4e0.1x)​=327​1+4e0.1x=94e0.1x=9−14e0.1x=8Dividing…

Q: 7 Let f(x) = Find f'(x). (8x2 + 2x – 6)* f'(x) =

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Q: Differentiate. f(x) = 7+ 3e5x f(x) = 7+15e5x O f (x) = 7+ 5e3x f (x) = 0+15e5x

A: Differentiate the above function.

Q: A2. If y = In10 10* then y'= %3D (a) x. 10*-1 (b) x10. In10 (c) 1 L 10* Ina

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Q: uestion 11 Given f(1) = 3. f' (1) = 8. g (1) = g' (1) = 9. find the values of the following. |=-1.…

A: Use the product rule and quotient rule of derivative:

Q: x² - 1 find f'(x) and f"(x). x2 + 1 (a) If f(x) %3D

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Q: Find f ogohif f(x) =, g(x) = x", h(x) = x + 3. 10 x+1'

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Q: Let Zlx) ~N(0,1) prop (x1.21) = %3D prop

A: Let X be the random variable from standard normal distribution with mean = 0 and standard deviation…

Q: 4. If f(x) = 7x - 3+ In x, then f'(1) = (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

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Q: 4) (y+*2)dx =xdy

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Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

Q: (i) 49s" + s = 0, s(0) = 24, s' (0) = 0. (ii) s" +9s = 0, s(0) = 6, s' (0) = 0. (iii) s" + 49s = 0,…

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Q: Differentiate. f(x) = (3x - 5) (Vx +4) O A. f'(x) = 4.5x'/2 - 2.5x-1/2 + 12 1/2 - 1/2 O B. f'(x) =…

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Q: L{f(at)}=(1/a)* f(s)

A: to prove the given problem . we use the definition of Laplace.

Q: Find h'(-3) if h(x)=4g(x)-5f(x), f(-3)-7,and g'(-3)=-2. Oh'(-3)-0

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Q: 2. f'(-0.1) -5.84 3. f'(-0.1) -5.74 4. f'(-0.1) -5.64 5. f'(-0.1) ≈ -5.54 (iv) Use p4 to estimate…

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Q: O Question 9 Find the derivative. g(x)=8x5 + x4-5x²+6, find g'(-4) 10.280 9.984 10.024 216 Question…

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Q: f(x) glx) f'lx) g'ix) 1 3 2 4. 6. 2 5 7 3 7 2 7

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Q: 6. у%3D (3х + 1)8 a. y' = 24(3x)7 оъ. у %3 3(24х + 1)" О с. у'3D 24(3х + 1)" O d. y' = 8(3x + 1)7

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Q: If f (3) = 5, g(3) = 2, f'(3) = 4, g'(3) = -4, and h(x) = 18. h'(3)? %3D what is 9(2). O 7 O -1 O…

A: f(3) = 5g(3) = 2f'(3) = 4g'(3) = -4

Q: Let g(x) = *-f(x) S(x) find g'(1), if f(1) = 4 and f'(1) = 2 c. - d. а. 2 b.

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Q: Find F'(x) given F(x)= (8t + 1)dr. a. F'(x)=1+8t b. F'(x)=1+&r c. F'(x)=8 с. d. F'(x)=5+&r? e.…

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