Equal 1 Amount (D+1)³ e* so much xe x'e r'e" 14 3

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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

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Q: 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

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Q: A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at…

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Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: 3. A kite holding a fixed altitude of 100 ft is pushed horizontally through the air by wind blowing…

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Q: 76. Use integration by parts to obtain the formula VT=* dx = +VT=x + 1 dx. 1 – x?

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Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

Q: 4(sinh 5. Evaluate 6 x) dx V1+x?

A: We use the well known formula for sinh^-1(x) = ln(x + sqrt(x^2+1)) and then integrate the…

Q: dN + N = Ntet+2 dt

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Q: sinh In(2+2x) dx? x+1

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Q: 2. A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being pushed…

A: Given, A ladder 10 m long is leaning against a wall. Bottom of the ladder is being pushed…

Q: 9. A man 5 n tall is walking toward a building at the rate of 3 A/sec. If there is a light on the…

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Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

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Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: One side of a right triangle is 150 m long and its adjacent angle is t/3 radians, with t/60 radians…

A: Use derivative

Q: 2. A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at10…

A: From the given data , Man walks across a bridge in one second AC=5 feet and boat passes in one…

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

A: Given that  Velocity of express train =40km/hr  Breaks apply at 50sec Retardation =0.5m/sec^2 To…

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

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Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

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Q: Use differentials to estimate the amount of paint needed (in m^3) to apply a coat of paint 0.04 cm…

A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

Q: •2 5. Calculate | x In(3x)dx.

A: Given integral:

Q: 3 sinº x dx 4 Show that

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Q: 9. S sec³ x tan x dx

A: Given ∫sec3xtanxdx We know that  ∫secx.tanx=secx + c ∫xndx=xn+1n+1+c

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

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Q: A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the…

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Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: To write the differential formula that estimates the given change in volume or surface area.

Q: How do you solve question 1?

A: The relation between volume of a sphere and the its radius is given as, Where  V: Volume r: Radius

Q: The bacteria in a certain culture increase according to dN/dt = 0.25N. If originally N = 200, find N…

A: Integrate the equation.

Q: 20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at…

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Q: Find the indefinite integral. ∫sec x/2 dx

A: Given ∫sec x/2 dx. We need to evaluate the above integral.

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Find the exact length from 1 to 2: y=((1/4)x^2)-(1/2)ln(x)

A: Find the exact length from 1 to 2: y=((1/4)x^2)-(1/2)ln(x)

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

A: Given

Q: Use differentials to approximate the quantity   √99.7

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Q: Use differentials to estimate the amount of paint needed (in m³) to apply a coat of paint 0.07 cm…

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Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: A quantity with an initial value of 110 grows continuously at a rate of o.5% per hour. What is he…

A: Given, Initial value of quantity = 110  It is growing continuously at a rate of 0.5%  per hour.  We…

Q: cosh(In x) dx

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Q: A Ball is thrown Vertically into the air at 120 m/s ,after 3 secanother ball is thrown.what initial…

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Q: 12. If the volume of a spherical balloon is expanding at a rate of 5im; How fast is the 4 radius of…

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Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 12 cm and height…

A: The volume of a cylinder is given by the expression . Thus the volume of a thin cylinder is obtained…

Q: A ball is thrown straight down from the top of a 370-foot building with an initial velocity of -18…

A: Given

Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

A:

Q: 3. Jメニ

A: We can find the antiderivative as below

Q: 2. The diagonal of a square increases at the rate of 3 m/sec. How fast is the area changing when the…

A: Let the length of diagonal be y. so that, Now, Length of the side of a square be x. Using the…