(e) Find the exact length of the curve. x = e cost, y = et sint, 0 ≤ t ≤n.

Q: Write the equation in standard form. x 2 + y 2 - 8x - 4y + 12 = 0 ( x - 4) 2 + ( y + 2) 2 = 8 ( x…

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Q: = 3. Let R be the region bounded by y = √x and y 2. Find the volume of the solid generated when R is…

A: Washer Method : Suppose that the f(x) and g(x) are continuous and non-negative function on a,b and…

Q: An elliptical plate, major axis 6 feet and minor axis 4 feet, is submerged vertically until its…

A: Follow the procedure given below.

Q: Q4: If f(x,y) = x²y +exy Siny Find 1) 2) (D = f) at po(1,0) in the direction of 0 = Po

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Q: A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution…

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Q: 033 110 A -1 2 3 Assume that AB=A+2B. Find the matrix B.

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Q: Q4:Evaluate 1) lim (1-1) x-0 \sin x

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Q: 13. Solve for x. log₂ (2x + 3) = 2 log₂ (x)

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Q: :S- 8x + 1 √4x-3 dx. If we let the substitution "=√√4x-5, the resulting integral Given : becomes Ⓒ =…

A: The integration of the integral is (8x+1)sqrt(4x-3).

Q: J udv = uv J to Explain why the substitutions below are inappropriate. Let U = eª and 1. Suppose we…

A: lets here we use integration by parts rule  ∫xexdx here lets u = x v = ex  is good to substitute…

Q: 9. Find the interval of convergence of the series n=1 5" (x-3)" √√n

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Q: estion 24 Copy of To integrate x³ ²dx' e+² x² Ox we apply integration by parts and in the form u dv,…

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Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2…

A: The region bounded by y=x and y=12x is rotated about the x-axis.

Q: 1. Given the function f(x) = 20 √7-x find f (-9). "

A: The given function is: fx=207-x    ...1

Q: (a) Find the slope of the tangent line to the given polar curve at the point specified by the value…

A: We have to find the slope of the given polar curve at the point specified.

Q: Question 4 A conical water tank has its top at ground level (consider this to be the x-axis) and its…

A: The given problem is solved below in detail.

Q: For the following function : 4 • <t<1 - f.(.t.)..==. [² 1<t<2

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Q: Enclosed by x² + 4y² = 16

A: We have to find area bounded by given curves.

Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: HOMEWORK 16: Graph the following equations. x3 3. y = (x-5)(x+1) x²14x13

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Q: Solve y' = 4xy - 2x, y(0) = 20 y(x) =

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Q: 14. Solve for x. 2¯¾ = 8(x-3)

A: Given, 2-x2=8x-3

Q: A fifth degree polynomial with constant coefficients may have (1) 5 distinct real roots. (II) 3…

A: This question can be solved by using the concept of nature of roots of n degree polynomial.

Q: To integrate x³ exdx'' X we apply integration by parts and in the form u dv, u is set as:

A: To integrate x3ex dx. We apply integration by parts amd in form of udv. u is set as

Q: 9) (3x-29 +2) ex+(39-2*-2) dyzo

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Q: y² = x and y² = 2 − x

A:

Q: (D² + 3D + 2)y= sin ex

A: The given differential equation is  (D2+3D+2)y=sinex

Q: Calculate (31-2). 051 0142 743

A:

Q: Find the radius of convergence, R, of the series. 00 (x-4)" n+1 n = 0 R = 1 Find the interval, I, of…

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Q: Solve the area bounded by the curve y=x^2+2 and the line y=-x, x=1 and x=-2. With graph

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Q: 00 country song NR6) If all of the letters in the word PENCILS are used, the number of arrangements…

A: Given ,  If all of the letters of PENCILS are used, the number of arrangement with all of the…

Q: 2. Given the following logarithmic expression: log, 1+ 2log 5 + log₂ 2 +log, c-log, 100 Which of the…

A: Given: logc1+2logc5+logc2+logcc-12logc100

Q: (-2xy) dx + (Sing-x)dy 3 7 dy + 3xy dx = x ēdx • (3x-2y + 2) dx + (3y-2x-2) dy zo (y + x² ) dx = xdy

A:

Q: and A solid is generated by rotating a plane region that is bounded by the curves y = 2² = y about…

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Q: 9. Find the indicated limit. lim (6x - 21)³ x-4 = Show any work necessary

A: Solution: As per given data   lim( x tens to 4){ (6x - 21)³} As per simple rule of limit go ahead…

Q: L 2 S 5 + 64

A: Laplace Inverse Transform of  function 5s2+64

Q: cln x e L L ² L the we Evaluate yez dz dx dy.

A: Given problem:-

Q: Find the area of the region bounded by the curves y = x²y = x² and ² 01/2 02 O 1/3 O 2/3 = xy = x.

A:

Q: Problem 3: ( >>> A bacteria culture starts with 500 bacteria and doubles in size every half hour. •…

A: Topic:- function  Note :- as per our guideline if more than three subparts posted than only first…

Q: Evaluate the integral. 4π S t² sin(2t) dt

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Q: (a) √738(t - 4)dt (b) 738(t + 2)dt (c) √²38(t+4)dt (d) f²3x²8(t-4)dt (e) ¹3x²8 (t+2)dt -3 (f) ²3x²8…

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Q: 8. Explain what transformations you would need to apply to the graph of y = f(x) to graph the…

A: In this question, We want to know the transformations that we apply to the function y=f(x) to graph…

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATION:

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Q: Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 -dx 2 √√3x²-4

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Q: (D² - 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

A:

Q: 15. y=Arccos (x²)

A: The given function is: y=Arccosx2   As we know that: The Chain Rule: fgx'=f'gx·g'x The Power Law:…

Q: Find the lower sum for f(x) = +4 on the interval [-4, 0] using 2 rectangles. 10 "F Submit your…

A: Here we have to find the left sum of given function.

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.…

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Q: The ellipse 3 4 8 16 x²y² 1 = + 9 16 4 has a vertical axis of

A: elipse equation is given  x2/9 + y2/16 = 1/4 here compare with  x2/a2 + y2/b2 = 1

Q: Problem 2: ( 3) Starting with the graph of y = e, find the equation of the graph that results from…

A: