(a) Show that the integral test applies, and use the integral test to determine whether the series converge or diverge. /2k k=1

Q: 6. Use Laplace transforms to solve the initial value problems: (b) x" – x' – 2x = 0; x(0) = 0, x'(0)…

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Q: x² + 2y? + 3z² 18. lim (x, y, 2) →(0, 0, 0) x² + y² + z?

A: We have to find the limit by two ways method

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Q: 3. Given r = t – 1 and y = t-2t, Eliminate the parameter and write an equation in rectangular…

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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Q: Q3) Find the Area bounded by the curves y? = x and x = 2y – y?.

A: The given curves are; y2=x & x=2y-y2   Now find the point of intersection between the curve y2=x…

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Q: From Rogawski ET 2e section 10.3, exercise 10. Use the Integral Test to determine whether the…

A: Given problem:-

Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of , does the curve has…

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Q: Question Consider the function f(x) below. Over what open interval(s) is the function decreasing and…

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Q: 1. Solve letter a and letter b. Show t complete solution. а. Find of the dy dx function 9x* + tany…

A: Topic:- derivatives

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Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: 12x 3 3 15 12 x4

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Q: Step 1 In pert (a), it was found that the two planes were 200 miles apart and getting closer at the…

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Q: Consider the parametric curve defined by 1=3+5t and y=1+3 Over which values of doesthe curve has a…

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Q: Let f(x) be the function 11a - 5x+4. Then the quotient f(8 + h) - f(8) can be simplified to ah + b…

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Q: 9. (D² – 2D + 5)²y = 0 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = –4 %3D -

A: We will solve auxiliary equation then we will find the solution.

Q: If Ax) = a(x-h)* +k, where a, h, and k are constants, find f"(). 2ax O 2(x-h) O ax+h+k 2a

A: The given function is f(x) =a(x-h)2+k,   where a, h, k are constant. We have to find f''(x) f''(x)…

Q: Find the absolute extrema of the function on the closed interval. h(s) = [0, 2] S-3 minimum (s, h) =…

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Q: From Rogawski ET 2e section 10.3, exercise 5. Use the Integral Test to determine whether the…

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Q: Q3) Evaluate triple integral (x - y²)dz dy dx.

A: tripple integral  First we will integrate w.r.t z and then w.r.t. y and then w.r.t. x.

Q: Activity 1 Find the antiderivative of the following functions. Show your complete solution and…

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Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: Differentiate the following functions. Show your complete solutions and emphasize your final answer.…

A: 1) f(x)=25x    Differentiate with respect to x   f'(x)=252) f(x)=-4x5+2    Differentiate with…

Q: Q3) Evaluate triple integral y(x2 -y?)dz dx dy.

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Q: wolloi or oisuleu 6. (-3x+15x") dx 12x 15 12 dx 7. + 3 x'

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Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

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Q: Find the volume trapped between the cone z = 2 – Vx² + y² (upper) and the paraboloid z = x² +y².…

A: We need to find volume.

Q: Find the equation of the tangent line to y = 7e* at x = 3. (Use symbolic notation and fractions…

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Q: 3rd derivative of y sin 3x

A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

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A: Let's find.

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2 y =

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Q: k=1 2K (c) Use the ratio test for absolute convergence to determine whether the series converges or…

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Q: Let r(t) = (t2, 1 - t, 4t). Calculate the derivative of r(t) a(t) at t = 4, assuming that a(4) = (9,…

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Q: Find the saddle pointis of the function f(x,y) = x° +y°+i y+4 Oa(5-1) Oc (4.0) & (4,0) Od(0.0)

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Q: Determine the equation of the tangent to the graph of y=x - 3x +x+3 at the point (- 1, -2). y 10x+ 8…

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Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x² + 16

A: To evaluate: I=∫dx9x2+16 Substitute x=4sec u3⇒dx=43sec u tan u du

Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: Evaluate the following integral using Partial Fractions Method: x³ + x? y = dx х2 + х — 2 -

A: Follow the procedure given below.

Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: Use the limit definition to compute the derivative of the function f(t) = , at t = -4. (Use symbolic…

A: This question can be solved using the concept of limit definition of derivative and equation of…