Find the limit. Use l'Hospital's Rule wher lim [In(x⁹ – 1) – In(x³ – 1)] - - *-1*

Q: Problem 3

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Q: 1. Find f(x) if f'(x)=12x¹+3√x+7-2e -4 and f(1) = 4

A: Given f'x=12x3+3x+7x-2ex-4  and f1=4 To find f(x):

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) [0, 6] x2

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Q: evaluate the limit, do not use lhopital's rule 1-x+2x+7 limx→-x 2 V 9x +5 - 3x

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Q: S [[x+1]], Determine iF f(x) = if x ≤ -1 2 tanh (H), ip-IxO (x+1), < <) In [cash (x+1) + sinh…

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Q: For F(x, y, z) = (x + yz) i + (y + xz)j + (z + xy) k, find: (a) the curl (b) the divergence

A: To find curl F and div F

Q: Solve for the solution of: (D3 + D)2y = 0

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Q: Find the domain and the range of the function. (Enter your answers using interval notation.) h(x) =…

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Q: Find the first four nonzero terms of the Taylor series about 0 for the function f(x) = √1+x cos(3x).…

A: We need to find polynomial series.

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: Find the nth Maclaurin polynomial for the function. f(x) = ex, n = 5 P5(x) =

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Q: Solve for the solution using variation of parameters: (D2-1)y= 2/(1+ex)

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Q: = ||r' (t) × r"(t)|| ||r(t)||³ to find (t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk Use the formula…

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Q: Find the tangent line approximation to the graph off at the given point. Then complete the table.…

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Q: f(x) = ((3x + 7) if x ≤ 4 ax-1 if x > 4

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Q: [2,

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Q: We can prove that if D is a region bounded by a simple closed path C in the xy-plane, then the…

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Q: x = 10t, y = t², (0 ≤ t ≤ 1). In each part, evaluate the line integral along C. NOTE: Enter the…

A: To find the values of given line integrals.

Q: Prove the identity. COS X 1-sin x 1+ sin x COS X Note that each Statement must be based on a Rule…

A: Solution )  cos x / ( 1 - sin x ) Multiply cos x in numerator and denominator =cos x × cos x /  […

Q: 27 SECOND DERIVATIVES Find TUTORIAL 22 if y-In (x + 1). Answer 2-2x² 22-2

A: Note:-As per your mentioned request i am solving question 1 from the given figure.

Q: A company that sells memory chips for computers established the price-demand and cost functions as:…

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Q: Calculate the length of the path over the given interval. (sin 7t, cos 7t), 0≤t≤n

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Q: (D² − 4)y : 4)y = 8e²x - 12 Your answer

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Q: Sketch the region enclosed by the curves x − 5 = 4y and x − 21 = (y – 4)², and compute its area. A

A: The given curves are; x-5=4y and x-21=y-42 Now find the point of intersection between the given…

Q: Homework 11 Parametric: Problem 5 Given ze and y = tet, find the following derivatives as functions…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: Homework 12 Polar: Problem 2 The limacon r = 1+ csin(0) has an inner loop when |c| > 1. (a) When c>…

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Q: Find all solutions of the equation in the interval [0, 2). sin x=√1- cos x Write your answer(s) in…

A: To solve the given trigonometric equation.

Q: Find a power series representation for the function. (Give your power series representation centered…

A: We have to find the Power series representation.

Q: A factory operating at maximum capacity can produce 25 fuzzles in one day. The cost of producing a…

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Q: 16. Let u = ln t, t = 2r and r = √w. Find and simplify du dw in terms of w.

A: As per Bartleby guideline,  we have answered only the first question. Please repost mentioning the…

Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: Find the solution to the following differential equations 1. ((D^3 +D)^2) y = 0 2. (D^2 - D - 2)…

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Find dy/dx by implicit differentiation. (sin mx + cos my)4 = 74 dy/dx=

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Q: Prove the identity. (secx+1) (secx-1)=tan ²x Note that each Statement must be based on a Rule chosen…

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Q: Write the Taylor series for f(x) = xº about x = −4 as Σ Cn (x + 4)". n=0 Find the first five…

A: The given function is  f(x)=x3 about x=-4.

Q: What are the cylindrical coordinates of the point whose spherical coordinates are (3, 5, 1)? r = 0 =…

A: Given: spherical coordinates ρ,θ,φ, here ρ=3,θ=5φ=π6 To find : cylindrical coordinates r, θ, z

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² = 100 Or-10 sin 0 Or- 10…

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Q: (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C…

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Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 27 - x, y…

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

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Q: Find the volume of the th

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Q: Solve xy = 8y - 3x, y(1) = −1. (a) Identify the integrating factor, a(x). a(x) = (b) Find the…

A: xy'=8y-3x

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +7 1 lim t +∞o (?, ?) 5t² + 6'5t,

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Q: = ||r' (t) x r' (t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7 sin(9t)j + tk Use the formula…

A: find curvature

Q: (a) Write a sum formula for sin(u + v + w). sin(u + v + w) = (b) Write a sum formula for tan(u + v +…

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Q: Find the area of the region between the curves y = 12 - x² and y = x² – 6. Area between curves =

A: To find the area between the given curves

Q: 17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Find in terms of x. dx 18. Given y = 5t (3 - t), t =…

A: Let's find.