Find the area under the curve y = 0.5x 15 from æ = 7 to a = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for æ > 7.

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A: Here we have to find the area of the surface given by z=f(x,y) that lies above the region R.

Q: Part 1: Let h be the height of AWXY. Find the length of the corresponding base. | cm 14 cm Part 2:…

A: Part 1  as h is height  base is WY length of base = 14 cm

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A: Follow the procedure given below.

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A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: Lena deposits $40,000 into an account that pays 6% interest per year, compounded annually. Ravi…

A: Given problem:- Lena deposits $40,000 into an account that pays 6% interest per year, compounded…

Q: Let g(x, y) = 3x²y + y³ - 27y

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Q: Determine whether the following series is convergent or divergente: (- 1)" n = 1 n'+5

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Q: Activity 1: Let's Compute! Directions: Investigate the discontinuity by using the three conditions.…

A: Follow the procedure given below.

Q: Simplify

A: Answer is no solution.

Q: Simplify cot(2 arctan 6). -35/37 -35/12 -1/6

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Q: help

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Q: 1. Determine the following using the graph of f provided below. If the value is infinite, specify ∞…

A: Solution: Given graph:

Q: dy х-1 The general solution of the differential equation dx y # -2 is y+2' О а. y² – x² + 2x – 4y =…

A: Topic = Differenial equation Correct option = c

Q: Q2/ Find S*(4 – 3x) sinx dx -

A: Given: I=∫0π/44-3xsinxdx   As we know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx And…

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Q: Evaluate the triple integral xy dV where E is the solid tetrahedon with vertices (0, 0,0), (6, 0,…

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Q: A ball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t…

A: Given query is to find the height of the ball at t = 5 second.

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: cos x dx 1+2 sin x

A: SOLUTION-

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y. (4, 0,…

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A: This question is based on integration by parts.

Q: Let g(x) = :| f(t) dt, where f is the function whose graph is shown below. What is the value of g'…

A: Let gx=∫0x ft dt, where f is the function whose graph is shown below.To determine the value of g'8.…

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

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Q: Simplify arcsec2.

A: Given,             arcsec2To find : Simplify

Q: ind, if any, the local maximum and minimum values and the saddle point(s) of the function f(x,y) =…

A: To find, if any, the local maximum and minimum values and the saddle point(s) of the function fx,…

Q: Find the volume of the solid generated if the region bounded by the parabola y2 = 4px (p > 0) and…

A: Given

Q: Given f(t) = 208e0.17t where 't' is in years, what is the continuous annual rate? Hint: Your answer…

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Q: Which of the following series is convergent? 2 n 3 n=1 3 n n=1 O None of them. n 4 n=1

A: Check the condition of convergence and divergence.

Q: Determine whether the following series is convergent or divergente: (-1) " n7 +5 n= 1

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by y…

A: Suppose f is non-negative and continuous on the interval [a,b],then the volume V formed by rotating…

Q: x- 1. a. Find the derivative of y =

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Q: Express the given equation in polar coordinates. 16xy = 121 121 ? cos 0 sin 0 = 8 121 r² tan 0 = 16…

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Q: 1. For each specified discontinuity, sketch the graph of a possible function f(x) that illustrates…

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Q: OR = {(r, 0): 0 <r< 6 cos(30), 0 < 0 < n}

A: Follow the procedure given below.

Q: Find the gradient of the function at the given point. Function Point F(x, Y, z) = Vx + y² + z? (8,…

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: For each problem, find the particular solution of the differential equation that satisfies the…

A: The given differential equation is: dydx=exy2 ; y-2=2e3+3e3e   As we know that; The Power rule:…

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify…

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Q: By the series test: n=1 n´ +6n+3 6.

A: To determine whether the given series converges or diverges.∑n=1∞5n2+6n+3

Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 1 is…

A: Use the disc method to find the volume of the solid.

Q: iut n=1 Find the radius R of convergence for the series

A: Just use the formula of Radius of convergence and find it. Radius of Convergences, R= 1

Q: Find the taylor series for f(x) about x=3 15) f(x)=x^3-10x^2+6

A: This question can be solved using the concept of expansion of Taylor series.

Q: d Calculate ri(t)· r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly and…

A: r1(t) =9t i + 2t2 j + 6t3 kdr1dt=9 i + 4t j + 18t2 kr2(t)=t4 kdr2dt=4t3 k

Q: Evaluate c (xy+y+z) ds along the curve r(t) = 2ti + tj + (2- 2t)k, 0Sts1. (xy+y+z) ds=| (Simplify…

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Q: Find the vector projv u if v= 5i +jand u = 2i+V17/

A: Use vector projection formula and dot product.

Q: S x²(csc2x³)(cot2x³)dx

A: