Si f (2) dæ = f (x) dæ – f f(x) dæ – § f (x) dæ - O True O False

Q: cln 3 Evaluate f" sech² t dt 15. B. ? c. A. D.

A: From the given problem: I=∫0ln3sech2tdt As we know that: ∫sech2(x)dx=tanh(x) And…

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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Q: Let y = [f(u) + 3x]^2 and u = x^3− 2x. If f(4) = 6 and dy/dx = 18 when x = 2, find f ’(4).

A: Given y=f(u)+3x2Differentiating with respect to x  dydx=ddxf(u)+3x2

Q: -1 If f(x) = 7 sin (x'), then %3D f'(x) =

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Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: sin, ifx T 2л

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Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

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Q: van fy = xy*-1 + x, ln(x) * f(x,y) = x + y* • if it was True false

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Q: X,X, X3 R.S. T3 %3D Bind dis tribution of Xo

A: Solution

Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: 1. S ef = c f

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Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: If f(x) is odd and ∫-1 to 5 f(x)dx=11 then, ∫1 to 5 f(x)dx=?

A: It is given that f(x) is odd and

Q: Let =)4.i8 0<x<1 f: [0,3]-R defined by fo %3D 3,if X=1 5, if <X< 3 show that feBra and thab fa.dx =…

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Q: tes, sno W inut E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 and

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Q: (c) Prove that 00 eiz = 0. (x+i)3

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Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: u (x ) =1-x – (x –t )u (t )dt X.

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Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: If f(z) = 3 sin (z) then f'(z) =

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Q: If f(x) = x² + cos(x), what is f" (x)?

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Q: 4. The two parts of this problem are related to each other. (a) Show by appropriate substitutions…

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Q: Assuming that f(x) dx = 3, F(x) dx = 5, and f(x) dx = 7, calculate f(x) dx. %3D (x) dx =

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Q: Find the value of (f o g)' at x = 1. Tu f(u) = cos u= g(x) = 4/x (fo g)'(1) =

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Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: Evaluate | f(x) dæ, where -T< x < 0 f(x) = 15 sin(x), 0< æ < n. | f(x) da = -T

A: Solve the following integral

Q: If f(x) = 7 sin x + 7 cos a, then %3D f'(x) = %3D f'(3) = %3D

A: Given functionf(x)=7sinx+7cosxdifferentiate with respective xf'(x)=7cosx-7sinx…

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

A: We have to find out

Q: 1. Find fr fy and fry if f(x,y) = y* + x?y + In xy.

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Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: off f(x) dx, where Evaluate [ f(x) f(x) dx = f(x) = 18x², -T≤x≤0 19 sin(x), 0≤x≤T.

A: We have to solve given Questions.

Q: If f (x) = eª sin x, then f' (x) A) et cos X B -et cos x c) e" (sin x + cos a) D) e" (sin x – cos x)…

A: We have to find the option

Q: Let f(x, y, 2) = eF tan(x² 2) . Compute fay: (x, Y, z) . Simplify your final answer.

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Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

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Q: If f(x) = 6 sin z + 6 cos z, then f'(x) = %3D f'(5) =|

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Q: If f(x)= tanh 1 et , then f'(x) is et 1- ex? 1 O 1- (e*)2 | et O 1-(e*)2 попе

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Q: If f(x) = tan(e²), then f"(x) = %3D A. 2e* sec²(e²) B. 8e*tan(e²) C. 4e* sec²(e*) D. 8e“ sec…

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Q: If f(x) = (e"1+z)' 15 sin(z) +8 cos(z) f'(0) then f(0)

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Q: If f f(x)dx si f(x)dx. 24. = 2; Sí f(x)dx = -1; ſ, f(x)dx = 7 , evaluate

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Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: Evaluate f(x) dx, where 8x', ={ 7 sin(x), 0<x< a. -T < x < 0 f(x) :

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Q: If F(x) -5 sin t dt, then F'(x) = %3D

A: Given: Fx=∫lnxex-5sintdt To determine: The value of F'x.

Q: Assuming that f(x) dx = 3, f(x) dx = 4, and f(x) dx = 8, calculate Fx) dx. %3D %3D Jo f(x) dx =

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Q: Prove that (x – 2)dx = – f,(x – 2)dx |

A: To prove that:∫13x-2dx=-∫31x-2dx

Q: Suppose that o f(x) dx = 3. Find , f(x) dx if, %3D

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Q: . If f(x, y)=x² cos y-y° sin x- xe" – ye* +2x²y² , show that ôxôy a²ƒ_ ô²ƒ дудх

A: Explanation and solutions is given below....