9. Compute the following: /е 1 1 (a) dax 1 x2 (b) Inx dx х

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

A:

Q: xe 2, x Cosz dx

A: Integration by parts, ∫udv=uv-∫vdu u is the first function Given integral, ∫x exdx

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: В. Estimate to three decimal places the value of: S V1 + x³ dx by using the trapezium rule with n =…

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Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: 4. y = 2Cos(x)Sin(2x) – Sin(x)Cos(2x) %3D

A:

Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: 2 9) -sinh? -cosh -dz

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Q: 2. Evaluate the integral: | sinh x cosh² x dx

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Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: sketch, eva luate freverse integ ration order of 2. 2. 4-X 2y e dy dx 4

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Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

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Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

A:

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

Q: Use a linear approximation (or differentials) to estimate the given number.   27.tan 2°

A: The Linear approximation of the function at x=a is given by L(x)=f(a)+f'(a)(x-a) To Find Linear…

Q: Use a linear approximation (or differentials) to estimate the given number. 99.8

A: To find √99.8

Q: 8. Approximate the value of xIn(x+1)dxusing left endpoints with n-4. Round to three decimal places.

A: We have to approximate given integral.

Q: Differentiate implicitly to find dz if xz + In(xy) + = 10.

A: Given an equation We have to apply the implicit differention to the equation

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional te…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the indefinite integral. S sinh (1 – 2x) dx

A:

Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

A:

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: 3. In (cose) tane de

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Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: The 32nd derivative of y = cos² 2r is O 26* cos 4x O -24 cos 2x O 24 sin 4x O 22 cos 2x

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Q: Use a linear approximation (or differentials) to estimate the given number. 99.6

A: Given query is to perform linear approximation on given redical.

Q: Suppose that a car accelerates at a rate of a(t) = t – 7 meters per second. Use the Fundamental…

A: ANSWER :

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: 1 point) Calculate the integral: 1 dx = (x + 8)(x + 4)

A:

Q: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

A:

Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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Q: Differentiate. y = In (7x + 8) In (8x + 5) dy dx II

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Q: 5. Explain in words what the output of sinh (y) geometrically represents. ule

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Q: Find y't yu 4=In(sec 9x +tangx)

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Q: What is the derivative of y = 10sin Sx 5 In 10 cos x 10sin Sx 5 In10 (10sin Sx ) A. В. C. 5 cos x In…

A: Given: y=10sin 5x To Find: The derivative of the given function.

Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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Q: 13) Estimate tan(44°) using linear approximation.

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Q: Find the indefinite integral. sinh(2 – 9x) dx

A: