00 3) Use the integral test to determine whether the series k=1 ke-2k diverges converges or

Q: y = ln(4x³ + 7x)

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Q: 5. Which of the following functions grows the slowest as x goes to infinity?

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Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: UX = Iz = uz = ly = Find the limits of integration ly, uy, Ix, ux, lz, uz (some of which will…

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Q: For y=5x^−2+8x^−3−7x−4, find dydx.

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Q: You have an investment of $22,400.00 that you want to double in 11 years. If interest is compounded…

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Q: 1. Determine the equivalent ODE by eliminating arbitrary constants y = ae-2x + bxe-2x Oy" +4y' + y =…

A: Given data:- y=ae-2x+bxe-2x

Q: TU 2. fz sin² x cos4 x dx J

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Q: Set up the definite integral required to find the area of the region between the graph of y = 13 –…

A: Concept: Area between the two curves: Let y=f(x) and y=g(x) be the curves and a and b are two…

Q: 2 √9x²-16 x² dx

A: We will use substitute method to solve the integration

Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: Suppose p′(−1)=−2 and q′(−1)=−5.5.  If r(x)=−7p(x)+10q(x), find r′(−1).

A: We have to find the value of r'(-1).

Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

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Q: Use following se k Z K-I the integral test Series to decide converge

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Q: 3 -2 7 4 3 2 1 -1 2 3 X

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Q: A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions…

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Q: Suppose that f(x, y) = e e-x² - 2y² + x Then the maximum value of f is

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Q: , b) Find the angle ZB.

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Q: Given r(t) = (set, et cos(t), et sin(t)), determine each of the following. (a) the unit tangent…

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Q: Break up 9 m/s 4.5 m/s [S], 7.8 m/s [W] 4.5 m/s [S], 4.5 m/s [W] 3 m/s [S], 6 m/s [W] O4.5 m/s [W],…

A: Please see the below picture for detailed solution.

Q: Let f(x) lim I→ 6+ if x = Calculate the following limits. Enter "DNE" if the limit does not exist.…

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Q: Find the radius of convergence, R, of the series. R = 00 I = n = 1 xn n45n Find the interval, I, of…

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Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: Determine the solution of the following differential equation: d²y dx² dy -8-+16y=0 dx where y(0) =…

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Q: Differentiate the following function. You do not need to simplify the derivative. F(x) = 4e²² F'(x)…

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Q: If 0 ≤ an ≤ bn and bn diverges, then an diverges. Select one: O True O False

A: This question is related to series and sequence, we will solve it using given information.

Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: Suppose an investment of $9,000 is invested at an annual rate of 9.4%, compounded continuously. What…

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Q: Evaluate are f(4) And solve f(x)=1

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Q: 1. Find the area under one arch of the curve y = cos- :cosex.

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Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

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Q: Use following series > k=1 the (+48 integral test Converge. to decide if th

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Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: Determine the infinite limit: O -∞ O 8 7-x lim x 4 x² - 2x - 8

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Q: 3. xy = a², y = 0, x = a, x = 2a.

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Q: d) f(a) = (2a-1)² 2a + 5a

A: Solution ) f (a) = ( 2a - 1 )2/2a  + 5a  We know that  ( a - b )2 = a2 - 2ab + b2 f(a) = (4a2 - 4a +…

Q: Assume the coordinates are integers. Determine the coordinates of the point shown. (Type an ordered…

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Q: di. Use v = L to find the voltage across a 30mH inductor at t = 5ms if dt (round final answer to 2…

A: By using v=Ldidt to find the voltage across a 30 mH inductor at t=5 ms if i=40 sin20πt-π6.

Q: Sketch the region enclosed by y = 5x and y = 6x². Find the area of the region.

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Q: 19. 2x³y = y(y² + 3x²).

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Q: Evaluate the limit of the given functions. 3x17x+ 20 lim. x44x² 25x+36 1. 2. lim t3 - 1 고 t-it-1

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: -) 5cos(x +40°) - 3.6 = 0

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Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

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Q: Use Mathematical Induction to prove the following. 1 Show that 1+4+7++(3n − 2) + (3n − 2) = n(3n-¹),…

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

Q: Use the graph of ƒ (x) = x² below to find a number & such that x² − 1| < 0.5 whenever 0 < |ï − 1| <…

A: The graph of the function fx=x2 is given To find the value of δ such that x2-1&lt;0.5 whenever…

Q: The volume of the box is 54 cubic inches. The material for the top cost $0.08 per square inch, for…

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Q: 10 5 f(x) 10 5 10 10 X

A: