Compute derivative for the of the

Q: x 5. r(x, y) = ln (x + y)

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Q: nd the solution of the given initial value problem: ) = || y(4) + 2y"" + y″ + 8y′ − 12y = 12 sin(t)…

A: The solution is given below

Q: A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 84°.…

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Q: Complete detailed solution. What is the equation of the tangent line at (0,0) of f(x)=2x²-3x

A: We need to find out the equation of the tangent line at the given point to the curve given.

Q: Find f[g(x)] and g[f(x)]. f(x)=√√x+3, g(x)= 18x² - 12 f[g(x)] = g[f(x)]=

A: To find out the f[g(x)] and g[f(x)]

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Q: Use polar coordinates to evaluate the double integral. 1 1 + x² + y² where R is the sector in the…

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Q: 1. Which function has the greatest average rate of change on the interval 1 ≤ x ≤ 3? Show all your…

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Q: 5. Evaluate 8y L L (PS4 12 dzdy + 1)² by reversing the order of integration.

A: Follow the procedure given below.

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Q: Shown is a graph of y=f(x) a) what is the transformations In the appreciate order of how to make a…

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Q: 5. For y = -ln(x), find the value of x where the slope is a) x = − 6 b) -In(6) d) Does Not Exist

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Q: Solve the differential equation. dr t In(t)r + r = 9tet

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Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution sets in interval notation…

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Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total…

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Q: Suppose that we have found a value of 8 such that ε = What numbers should go in the blanks such that…

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Q: Determine whether the series below converges or diverges. If the series converges, find its sum.…

A: Expand the given summation

Q: Find the volume generated by revolving the area 1 bounded by y = " x³ + 16x² + 63x (Round the answer…

A: We need to find volume.

Q: xp (I + ²)² [ (1) 9x)x I

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Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

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Q: gral Izyds xy ds ere C is the spiral r = e from 0 to 0 = 2π. =

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Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2rs, s² - 6r). Use the table of…

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Q: 3. Let S be the surface defined by the vector function R(u, v) = (2e" sinv, 2e" cosv, u²+u), Find an…

A: This is a problem related to vector calculus. Please follow the general procedure given.

Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Evaluate…

A: Calculate value of function at given points  Then calculate difference between the values of the…

Q: The piecewise function /(x) is graphed below. Use geometric formulas to evaluate the following…

A: First we find f(x) , Here in interval -7≤x≤-1 f(x) is semi circle, whose center is at (-4,0) and…

Q: Fill in each blank with an angle between 0° and 360° such that sin 220° = sin and cos 220° = cos 0

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Q: This answer is w

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Q: The function s(t) = t³ - 12t² + 45t represents the position of a particle (in meters), at time t (in…

A: We have to find points of position where object is at the rest position.

Q: Suppose f(z) represents the total number of children that have a symptom, and z is the number of…

A: We can answer both the question as below.

Q: Use a graphing utility to approximate (to three decimal places) the solutions of the equation in the…

A: Using ÷ cscx=1sinx   1sin2x-8=0 1sin2x=8 sin2x=18 Now taking inverse and finding values of x we get…

Q: where do these (encircled in red) come from?

A: I am attaching image so that you understand each and every step. Please take exact value then we get…

Q: At what points on the given curve x = 2t³, y = 2 + 10t 14t2 does the tangent line have slope 1? = (L…

A: Given problem:- At what points on the given curve x = 2t3 , y = 2 + 10t - 14t2 does the tangent line…

Q: Solve the right triangle with hypotenuse 28 and one of the acute ngles 42°.

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y² + 8, (2, 4) Vf(2, 4) = (No…

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Q: Determine the length of the parametric curve given x = 6 sint, y = 6 cost, ㅠ 0 ≤ t ≤=.

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Find the exact length of the curve. x5 1 6 10x³ y = + 1 ≤x≤ 3

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Q: w = xy cos z, x = t₁ y = t5, z = arccos t (a) Find dw/dt by using the appropriate Chain Rule. dw =…

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Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution sets in interval notation…

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Q: (b) ^ / dx a² I

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Q: Evaluate

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Q: Determine whether the following series converges or diverges: 2. 1. +00 Σ n=1 1 + sin2n] 10n +00 ΣΕ…

A: We need to determine whether the given series converges or diverges

Q: The Cartesian coordinates of a point are given. (a) (-2, 2)

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Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (x²+x-14) = 6…

A: To prove  limx→-5x2+x-14=6 , we need to prove that    for any ε>0     ∃  δ>0  such that…

Q: f(x) Suppose that f(x) and g(x) are differentiable functions such that f(7) = 2, f'(7) = 6, g(7) =…

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Q: 1- Consider the following nonlinear 10x - 3+e-³-2³ sin(x) = 0. a) Prove that the nonlinear equation…

A: GIVEN:- 10x-3+e^(-3x)-x^3sin(x)=0

Q: +∞ Σ n=1 (x + 1)" 3°/m² + 1

A: Given Power series,∑n=1+∞x+1n3nn2 + 1

Q: 20. Find the area of the region outside the circle r = 3 and inside the circle r = 6 cos 0. -2 0 -2-

A: Given curves are r=3 and r = 6cosθ  At the point of intersection , we have…

Q: Differentiate implicitly to find dy/dx. sec(xy) + tan(xy) + 10 = 1 (No Response) dy dx

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Q: Solve 8 sin (7x) = 7 for the four smallest positive solutions

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