Determine whether the integral is improper L' (x-4)-¹dx (A) Not improper (B) Improper

Q: 2. x*+5x³+20x+16 x(x²+4)² √x*+5x² dx

A: First of all, we find the partial fraction decomposition of  x4+5x3+20x+16x(x2+4)2

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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Q: d [rı(t)- r₂(t)] = [ dt d [ri(t) x r₂(t)] = dt

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Q: Evaluate the limit A. ƒ(x) = 5x + 2 at x = 3 x²-9 B. f(x) at x = 3 x-3

A: A. f(x)=5x+2B. f(x)=x2-9x-3

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: ANSWER

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Q: 18. Applying the sum (difference) rule, what is the derivative of the given function? F(x) = sin x…

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Q: Solve for 0 <0 < 2π Separate your answers with commas. 0= sin 40+ sin 50 = 0.

A: Here, the given equation is: sin 4θ+sin 5θ=0...(1)

Q: 6. 22x+x dx

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Q: he equation of the line that passes through the point (-4,-2) and is parallel to the line y=4x-8 is…

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Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Evaluate the iterated integral. 18 5 (x + y²) dx dy

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: 18. In each part, evaluate the integral, given that f(x) = (2x, x≤1 x>1 2, (a) forex f(x) dx (b)…

A: 18.fx=2x,x≤12,x&gt;1

Q: 1 Use the inverse matrix -5 5 x + y + Z = 0 5x + 7y + 6z = 4 5x + 8y + 7z = 2 (x, y, z) = = ( 1 -1…

A: Given the inverse matrix is  11-1-52-15-32. The system of linear equations is…

Q: The base of a three-dimensional figure is bound by the line y = -x + 1 on the interval [-3, 0].…

A: Solve the following

Q: 2. x' + - y3 = 1, D2y 3

A: Given :

Q: Find the laplace transform of ƒ (t) = 2t³ – 6t – 8 -8s³+12s-6 OF (s) = 84 OF (s) 6s³-8s-12 84 ○ F…

A: Given that,  f(t)=2t3-6t-8

Q: Evaluate the following x4 (5-x²) dx

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Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for f(x) = √√x + 4 on the…

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Q: L=

A: Follow the procedure given below.

Q: Find the laplace transform of f(t) = 6t³ + 4t² 3 F (s) = F (s) F (s) = F (s) = F (s) F(s) = -85³ +…

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Q: The function f is defined as follows. 2x if -2<x<0 f(x) = x³ if x20 (a) Find the domain of the…

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Q: A Cessna plane takes off from an airport at sea level and its altitude (in feet) at time t (in…

A: Given: ht=2000lnt+1 Rate of climb will be rate of change of height i.e. dhdt

Q: 2 The √tan x secxdx is {A} tan³/2x-tan7/2x + C {B} tan³/2x + ² tan7/2x + C {C} tan5/²x + tan7/²x + C…

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Q: 3. What is the FIRST derivative of the given function? y = 3x³ - 2x² + x - √√2

A: Given,            y=3x3-2x2+x-2To find : What is the first derivative of the given function.

Q: Find the derivatives of the following function (a) y=4²-3+2√ 2x+3 (b) y=2

A: We can answer the questions as below to find derivatives

Q: Find T(t) and N(t) at the given point. T() = N K2 r(t) = 9 cos(t)i +9 sin(t)j + tk; t= 2 =

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Q: The cos³dy is {A}-sin+sin³+C 3 3 3 4 {B} sin¹-sin³+ C 3 4 3 4y (C)-sin-sin³+C {D}sin+sin³+ C

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Q: Income flows continuously into a manufacturing company at the rate of 36, 450e 0.052t dollars per…

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Q: Evaluate: sec²(4t) [3-tan(4t)]³ dt a.-16 [3-tan(4t)] + C b. | [3 –tan(4t)] + C 4 OC. 1 [3-tan(4t)]…

A: integration

Q: limn o 9-h-3 h 1 6

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Q: Plot y = B sin(Aπx) cos(x) with a solid line over the interval 0 < x < 3 with the vertical axis set…

A: close allclear allformatclc A = 21;B = 5;C = 3;y1 = @(x) B * sin(A*pi*x) .* cos(x);y2 = @(x) B *…

Q: Test the series for convergence or divergence. n+5 Σ n=1 n³-1 Show all work using the limit…

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Q: 2. y = x² sinx What is the appropriate formula? dy Solution:

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Q: Consider à = (2,1,k), and b = (k,-8,k). Find the value of k such that å and bare perpendicular.

A: We can find the values of k as below.

Q: thout eliminating the parameter t, find a Cartesian equation for the line tangent the curve C,…

A: Given the query is to find the equation of the tangent.

Q: Show that if x is an integer, then gcd (x+1, x^2 -x +1) divides 3. Use this result to find knowing…

A: Solving

Q: The following symbol represents the derivative of a function EXCEPT one. Select the correct…

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Q: - x³ + x² + 2x + 1 (x² + 1)(x² +2) da

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Q: 7. ft³10t+-3 dt

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Q: 25-28 Use Theorem 5.5.4 and appropriate formulas from geometry to evaluate the integrals. 25. L²₁ (4…

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Q: y = 3x-2\4 4x-5

A: WE use the properties of logarithm to find the derivative

Q: Evaluate the following: 1) S x² √1 + x dx

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Q: 2) √ x¹ (5-x²) dx

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Q: Use the formula k(t) = = k(t) = ||r' (t) x r"(t)|| (t)||³ ||r' r(t) = t²i+t⁹j = to find k(t).

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Q: Find the limit. NOTE: Enter the answer using round brackets. 1 lim (12²2 +9.7) = (17.00) 9't

A: Given : A value that a function approaches the output for the given input values Here, it has been…

Q: 1) Use the Integral Test to determine whether the series Show All Your Work! n 2 n=1 n° +1 is…

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Q: Question 9 Find the simplified form of the derivative of y = Š Oy= 3 csc 3 CSC (3x) 3 csc 3z = cot…

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Q: x² +9+√√√y²+1=5 max x + y

A: Given problem:-