Use the log rule of differentiation and differentiate y with respect to x.  y = ln( 8 + ex 8 − ex

Q: Evaluate the definite integral. sin(3t)dt

A: I=∫0π3 sin(3t) dt  =-cos(3t)30π3  =-13 cos3π3-cos0

Q: Use linear approximation, i.e. the tangent line, to approximate V16.2 as follows: Let f(x) = Va.…

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Q: The Trapezoidal Rule ou e id b oblw Jeot en f (x) dx = h +f(x1) + f(x2) + ..+ f(xn-1) +f(xn)) b-a…

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Q: initial deposit of $1,000 is placed in a savings account with an APY of 4.3% sume the interest rate…

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Q: Find the volumes OF the solid generated by revolving the regions bounded by the graph Of the…

A: Volume of revolution

Q: 20 . Using the definition of derivative at a point, f'(9) f(x) – f(9) x – 9 Let f(x) lim enter %3D…

A: Given: fx=20x It is given that definition of derivative at a point x =9 is defined as…

Q: An inverted pyramid is being filled with water at a constant rate of 65 cubic centimeters per…

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Q: ind for by Implicit differchtioution 2(xu)

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Q: Let ü = - 4 and i 3 , and let w = ü x v. Answer the following: Find w. Give your answer as a vector…

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Q: Find the fourier senes for the Periodic extension given below! te [o, 2] X (t) = -1 te [2,4]

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Q: dy Then find the slope of the curve at the given point dx Differentiate implicitly to find…

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Q: A plane P, in R'is perpendicular to the vector n = (6, 2, 8), and contains the point (– 9, – 1, –…

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Q: Use polar coordinates to evaluate the double integral of y(x^2+y^2)^2 dA, where R is the region…

A: Let's find.

Q: * Your answer is incorrect. Use Green's Theorem to find the work done by the force field F(x, y) =…

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Q: u-3 15) If y= u+4 and u = 2/x+ 2, find when x = 7 dx %3D

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Q: A rectangle sign has a perimeter of 72 ft and an area of 320 ft2. What is the length and width of…

A: Solve the following

Q: Find a plane through the points (4,-3,-4), (-6,2,8), (3,-8,8)

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Q: Use Stokes' Theorem to evaluate F- dr. F(x, y, z) = xyi + x*j+z?k where Cis the intersection of the…

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Q: 11r If F(r) and o is the surface (x – 4)2 + y² + z² = 49 oriented 3 outwards, what is the value of…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

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Q: |A:k||2||Br:||2) < ||A||F||B||F k=1

A: answer is in next step

Q: ydy V2y-1

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Q: Verify the formula LF a ds = S cdiv F dV in the Divergence Theorem by evaluating the surface…

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Q: 3) Ernie the African Elephant is 9 feet tall and weighs 6 2 tons. Elijah is a similarly-shaped…

A: Unitary method: The unitary technique entails first determining the value of a single unit, followed…

Q: 16 d :| (2V8– 1) dt da. valuate dr. dx 5.

A: We have evaluate to the given expression

Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

Q: Find a particular solution of the DE: y" – 6y' + 8y = 64x?. C. yp = 8x + 12x + 7 E. None A. Yp = 4x?…

A: Solve it

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x2 - c and y = c – x² is…

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Q: Find the area of the region bounded by the curves x=y3 and y=x2.

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Q: Consider the double integral XY dA Vx2 + y² I where R is the region of the XY plane, given in the…

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Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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Q: Find the area of the shaded region 10x) = 8x - 2x - x, g0x) = 0

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Q: you save 270 PER QUARTER for retirement in an account that earns 8% interest per year compounded…

A: Given query is to find the amount accumulated.

Q: 2)Consider the parent function y = x^2. For each function below, describe the transformations which…

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: -dA dV dp 1. It shows that the behavior of fluid is A From the equation stated, show the formula +…

A: Here we have taken constant acceleration d2sdt2=dVdt To find the value of particular solution s(t)…

Q: Let f(x) = x^2 . Describe a series of transformations which could map f(x) onto g(x). Then write an…

A: Here we have to do the transformations to the graph of f(x) so that it mapped on to g(x).

Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: sinex) sintpx) x

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Q: Determine the area of the region bounded by x = y2 – y -6 and x = 2y +4.

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Q: Water is pouring into the conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

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Q: Klara is building a fence in her backyard. The sides of the fence will form a right triangle with…

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Q: Let T: R - R be a linear transformation such that T(1, 1, 1) = (4, 0, -1), T(0, -1, 2) = (-5, 4,…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Sketch the region enclosed by Y 6x and y = 9x". Find the area of the region.

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Q: Given the function f(x) = 3x – 1 f(r + h) – f(x) Find the difference quotient h f(x + h) – f(x) Find…

A: We have to find following value.

Q: 2 Integrate | 20(5æ – 3)°dæ - – 2

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Q: Apply differentiation rules (PRODUCT RULE) to find the equation of the line tangent to the graph of:…

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Q: Mark the critical points on the following graph. | 20- 16- 12- -5 -4 -3 -2 -1 2 3 -4 --8- -12- 16

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