5. Prove lim,40 V2r +I= 1.

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Q: 3. (1 + e**) + e (1-- 0 Ans. x + ye*/y = C

A: To differentiate.

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A: We need to evaluate integral.

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Q: Mathematics

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Q: 17. y csc(5x)

A: Differentiation

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A: This question is related to equation of straight line, we will solve it using given information.

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A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

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Q: Evaluate the definite integral. I' i+e¯*j+tk )dt O !! k 11 (ell – 1) i – (e- – 1) j + - k O ell – 1…

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Q: x +k a. Determine the value(s) ofk such that g'(1) = 5 if g(x) = %3D %3D x² - 2

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: x-1 y = log x+1

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Q: The solution y, of the homogeneous differential equation y() + 36y" = 0 is O None of them O c_1+c_2…

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Q: 25 Type the correct answer in each box. 37 The vector \ / Is reflected across the line Y = 1 and…

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Q: find the y a) y= CtX_ メ

A: As per guidelines we have to solve one question Please repost other questions again

Q: P6: x2 dx 2 – 1

A: We have to solve given integration

Q: x3 + x2 – 5x + 15 dx 5. (x2 + 5)(x² + 2x + 3)

A: Partial fraction: A complicated rational statement is decomposed into two or simpler fractions using…

Q: A 1.Find the domain of following functions: a.f (x) = {(2,6), (3, 9), (7, 11), (4, 0), (-1, 12)} and…

A: We are asked to find  domain and composite of the function

Q: Without evaluating the constants, the partial fraction decomposition for 5x? – 3 - f(x) %3D (x3 –…

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Q: [a csc ()- y] do + ædy = 0 CSC O y= x cos(In z) + C O y=D cos (In a + C) O In + cos(E)= C O Ino COS

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Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

A: Given:  xy3dx+(y+1)e-xdy=0xy3dx+(y+1)e-xdy=0(y+1)e-xdy=-xy3dxDividing equation on both sides by…

Q: |y = xx² – 4)

A: This is a problem of area calculation by region given. Based on the general formula and concepts we…

Q: Test the series for convergence or divergence. 3 3 3 11 3 3 10 12 13 O convergent O divergent

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Q: 8- Consider u=x², v=1/u+1 and w=vv find dv/dx

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Q: Without evaluating the constants, the partial fraction decomposition for 5x? – 3 f(x) %3D (x3 -…

A: Given :5x2-3(x3-4x)(x2+3x+2)(x2+1)

Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. find a potential function for…

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Q: Q2/ Find the second derivative of the following: 1. 2 Va 2. (x-1)(x2-2x)

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Q: Part 2: Differentiate the following functions. Show your complete solution. 1.) (x) = (x +3x)1000…

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Q: Find the length of the curve 7(t) = (4t, In(t), 4t²) for 1 <t< 4 Add Work Submit Question

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Suppose the table below gives the velocity of a moving object at any time t. Note that 7 IS measured…

A: We have to find the distance and graph of v(t).

Q: The solution y, of the homogeneous differential equation y() +36y" = 0 is None of them c_1+c_2 x+c_3…

A: We have to find solutions

Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x² + 2)| + C…

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Q: In(n+24)158 In(103+12 n)200 The sequence is and its limit is

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Q: A. Solve the following problem involving derivatives 1. The position of a particle is given by the…

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Q: II. Find the equations of the tangent and normal lines at the point indicated. a. 7x - 6V3ry + 13y -…

A: Solution is given below:

Q: Differentiate x + y = e2x+2y A. 1 – 2e2x+2y 1+ 2e2x+2y y' В. -1 + 2e²x+2y 1 – 2e2x+2y y' | С. ||

A: Given query is to find the derivative of the expression.

Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: Using the substitution x = sec 0, 2dx Jx?Vx² – 1

A: We can find the solution to the integration as below.

Q: Find the nth term of a sequence 2,5,10,17,26, ...

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Q: Without evaluating the constants, the partial fraction decomposition for 5x² – 3 f(x) (x³ – 4x²)(x²…

A: We have to solve partial fraction.

Q: 1. Find r(9/2)=? 2. В (3, 2) %3D?

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Q: For some constant a, the following improper integral | (x2 – 1)e2xdx converges to converges to e2a…

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Q: Determine whether the series is absolutely convergent, conditionally convergent or divergent. Please…

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Q: 4 Which of the following is the correct expansion of (3x - 3y)2? 9 x2 - 18 xy + 9 y2 9 x2 - 9 y2 9…

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Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

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