dy 1- Sinx+ Cos2y3D0 dx

Q: Evaluate the integrals for 16 sin²x cos²x dx X,

A: Given ∫16sin2x cos2x dxTo evaluate the integral:

Q: Using linear approximation formula, approximate ln(1.02) 0.02 O 1.02 O In (1.02) O In (0.02)

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Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

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Q: 7L 1 Se cos 2t dt

A: Given,            ∫e7tcos2tdt

Q: xe dy + *+1 dx = 0 ㅇ (1- y) e" + 빨고 =C O (y – 1) ev + + In a = C 2 O - (y + 1) ev - + In r = C O 2y…

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Q: cln2 e-x dx 0.

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Q: Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder.…

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Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(3,-2, 2), Q(5, 1, 5),…

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Q: Evaluate the following integrals. Show all the necessary or complete solutions. 3/2 4. S x²ca²- x²)…

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Q: sin III. Use Squeeze Theorem to evaluate lim In r x→0+

A: This is a problem related to limit and continuity of the function. Based on the general formula and…

Q: S(x² – 1) Vx + 4 dx 4.

A: 4.∫x2-1x+4dx

Q: Q2: Find a root of x – 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that…

A: We have to find the root of given function by Newton Raphson method.

Q: Use the Integral Test to determine vhether the series converges or diverges. ke -8k k=1 Evaluate the…

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Q: Find all critical points of the function ƒ(x) = 5x2-2x+12 (Use symbolic notation and fractions where…

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Q: II. Consider the function g defined by 1 g(x, y) = cos (TxVy) + log3(x – y)" Do as indicated. 3. In…

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Q: 60 50 40 30 20 10 -10 10 20 30 Victoria is a lifeguard and spots a drowning child 30 meters along…

A: We need to find distance of jumping.

Q: れ ポ+n3 lim (nj)2 + n4 j=1 n-00

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Q: dx coSX dy= 3 Cosx dx ( 3x+2)

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Q: Obtain the general solution unless otherwise instructed 2. у" — у' — х — 0 SUMMARY OF ANSWERS 2. Yc…

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Q: 1. J (5x* - – 4x + 7) dx 8x³ + 6x2

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Q: Consider the two series: 2n + 3 (а) n² In n n=1 00 1+ (n – 1)! (b) E n! n=1 Which of the following…

A: 1) Hee, note that the first series first term it self a infinity.

Q: Given the equation dx + xydy y? dx + ydy. Solve for the solution when x = 3 and y = 0 1. ( ) dx ) dy…

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Q: A curve is defined implicitly by the equation ax + by2=r2 Given that a=20, b=2 and r=7, find the…

A: We have to find the solution.

Q: A ball is thrown vertically upward with a speed of 15 m/s. Determine the maximum height and the time…

A: Find maximum height and time to reach that's height

Q: Using L'Hopital's rule, calculate the following limit: T-sin r lim, 0 O 1/6 O 1 O does not exist

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Q: Find all solutions to the equation. 2 sinx- cosx=1 Write your answer in radians in terms of t, and…

A: Given: 2sin2x-cosx=1   As we know that; The general solution of the trigonometric equation cosx=cosα…

Q: y+8y+5 (y-1)(y+1)(y2+8)2 Integration by Partial Fractions

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Q: dy Siven the equation below, find dz 16z° + 2ay + y° = 19 24. dy de low, find the equation of the…

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

Q: Find the gradient field F of the function f. 7 8 f(x.y,z) =x°e x +y'z O A. F= (5+8x)x*e *i+7y®j+8z°k…

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Q: For the function shown bellow; Find the second order derivatives : af/ay (a^2 f)/(ay^2) f (x, y) =…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The ladder 7.5 meters long is leaning agains the wall of a house.  The base of the ladder is being…

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Q: -olve for two cases csc² 20 cot 20 de irst case Using u = cot 20

A: Topic:-  integration

Q: A. Plane Area in Rectangular Coordinates Find the area bounded by the given curves. Sketch the…

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Q: Express the following sum.. using sigma notation. 1 d. 9 1 Σ 12 + + + 10 11 k= 1

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Q: Scos | cos 3x cos 4x dx :

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Q: 2 Find the definite integral fo5 tan(x)dx using strips of width for the trapezium rule correct to…

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Q: Evaluate tne derinite lntegral. 3 3 (9t – 4) dt 2 (일-(1 (9(9) )(a) - (20 - aco) 9(0) Therefore, the…

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Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4r + 2y + z subject to z?…

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Q: Find the volume of the solid above the region D={(x,y) : 0s Xs V27, 0s ys 27-x2) and between the…

A: Let's find.

Q: 4(-0.1)(120)= 12 니

A: The simplication is given below:

Q: Find the dimensions of a rectangle with perimeter 200 ft and whose area is as large as possible. O…

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Q: 3. J

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Q: = csc() – y] dæ + ædy = 0 C CSC Dy = = cos-' (In z + C) O Ina + cos () = C O Inz (금) =C cos Oy = x…

A: Topic:- application of integration

Q: Given the following vector field and oriented curve C, evaluate F•T ds. F= (-6y,6x) on the…

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Q: Q1) Using numerical integration to estimate the area (r=4 )and c(4,0) with n=4 of the semicircle

A: Trapezoidal rule: One of the most significant integration rules in Calculus is the "Trapezoidal…

Q: Evaluate the integrals in the following questions using integration by parts For |0 cos cos T0 do

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Q: 2. S

A: Given :∫xdxx2-4x-7

Q: Find the slope of the tangent line to the curve given by x + y° = 2 at the point (1, 1) -1 O 1

A: find the slope of the tangent to the curve x5+y5=2 at (1,1)   d(xn)dx=nxn-1

Q: For the following function, find its inverse. f(x)= ln(4x−2)(4x−2)   a. f⁻¹(x)= (eˣ - 4)/3 b.…

A: We have to find the inverse function

Q: For the given functions, identify the horizontal and/or vertical asymptote(s). Then write the domain…

A: Let's find.