Calculus Question

Q: Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D |…

A: Given

Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx

Q: Use a triple integral to find the volume of the solid in the firsy octant bounded by the coordinate…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: Find r'(t). r(t) = 6 cos (t)i + 3 sin3(t)j + k r'(t) =

A: Let's find.

Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

Q: Find the area of the region inside the circle r = 24 sin 0 and outside the cardioid r = 8 + 8 sin 0.…

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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: Question 18 Find the surface area of that portion of the surface 2 = V4 -x that lies above the…

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Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= <0,-8,1>+t<5,0,5>

Q: Two particles travel along the space curves r(t)and u(t). (If an answer does not exist, enter DNE.…

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Q: 1009 1010 Suppose R= E (2k) = 2 + 4 +6+.+2018 and S= D (2k-1) =1+3+ 5+.. + 2019 What is the value of…

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Q: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

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Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

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Q: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) j+…

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Q: 27х3-8а3 y3= y= 3x-2a Зх-2а

A: Y'=?

Q: Question 11 /4-x² c 3-x²-y² STS xdz dy dx Evaluate the iterated integral. J. J. -5+x²+y? 0, A)…

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Q: Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as…

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Q: 1- sine Evaluate the iterated integrals J. J. r2 cose dr de̟ A ) 1 В 2 (c) o D 3

A: The integration of the double integral is r2Cos(theta).

Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

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Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

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Q: e

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Q: The point P(8, - 10) is on the terminal side of an angle e in standard position. What is sec(e)?

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

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Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different way dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: Consider the following functions. f(x) = 4 sin x g(x) = 4 cos 2x Sketch the region bounded by the…

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

Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Find the following for the given equation. r(t) = (e, 5t?, 6 tan(t)) (a) r'(t) = (b) r"(t) = (c)…

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Q: Evaluate JJ xy dA , where R is the region in ху ´(1, 3) (5, 3) R (2, 1) (4, 1) A) 56 в) 67 38 D) 90

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

Q: Show

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Q: Question 17 Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the…

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Q: Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

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Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

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Q: 1-sine Evaluate the iterated integrals J. J. r2 cose dr de A) 1 B 2 c) o D) 3

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Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Question 13 Evaluate JJ xy dA , where R is the region in fa, 3) (1, (5, 3) R (2, 1) (4, 1) x A 56 В)…

A: A detailed solution is given below.

Q: 1) lim x100+500 ex

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

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Q: Find the center of mass of the given system of point masses lying on the x-axis. - 6, - 3, m,- 6 X1…

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Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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