Question 3 хаx S- can be solved by either algebraic subsitution or integrataion by parts. x- 1 T True F) False

Q: Q3) Evaluate triple integral Lyx -y)dz dy dx.

A: Topic = Integration

Q: olve the following Initial Value Problem: y" + y-6y 0, y(0) = 2 y (0) = -1. and %3D %3D %3D

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Q: dy Given 4x -9y =1. Find by implicit differentiation. dx

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Q: Helene invests Php 5,000 in an investment that earns 6% per annum. How many complete years doe it…

A: Topic = Algebra

Q: Give the VALUE only. No need to inclu unit. *

A: Given: s=24t+10t2

Q: nsider Evaluate дхду

A: Given,             z=ex3+y2To find : Evaluate ∂2z∂x∂y

Q: sin x Let g(x) = 1 ot. Find the derivative d'(x). '2 1+t3 none of the choices cos X 1+ sin3x sin? x…

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Q: Q5/ Use Linear Regression to fit the following data: 1 3 4 Y 4 9 10 10 8. 00

A: Follow the procedure given below.

Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 and whose normal line…

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Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Find the absolute extrema of the function f(x)=(x+1)*" in [-2,1], if there is any.

A: f(x)=x+123

Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

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Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Let's find.

Q: g"(x) sin(x- 1) x-1 -4 13 A(x) = kr -8x + 6, -1 10 x>3 8 3 -1 (E) Find all x value(s) on the open…

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Q: Determine an antiderivative, y, of the given derivative, y. Then use the given condition on y to…

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Q: sin x xý + 3y += x2

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Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

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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: ) Evaluate f'(x)dx.

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Q: +1

A: I have stated the used formula in the solution

Q: 2 dr sech 2r= e2r +e-2r A) True B) False

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Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: dy Find given x'+y' =8xy. dx Note: Enclose all terms in a parenthesis if either the numerator or…

A: Here, the given equation is: x3+y3=8xy...(1)

Q: 1 Solve the integral: 1+x + C + C C) None of the given choices 5. Inl + C 56

A: Let's find.

Q: .2 dx I (w² – 25)5/2

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

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Q: | cos ?x sin'x dx can be evaluated by factoring sin'x as (sin²x) ²sinx and transf sin²x into 1-…

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Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 => (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: dx Evaluate: (x-4)(x-1) X-1 + C x- 4 A B None of the given choices 3ln + C x-4 - 4 + C x- 1 D X- 4 E…

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Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

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Q: Jse the vectorized Euler method with h = 0.25 to find an approximation for the solution to the given…

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Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1

A: ∫xdxx-1

Q: %3D /Q5) Find volume of body bounded by z2 +y2 + x2 = 4.

A: To find the volume of the body bounded by z2+y2+x2=4.

Q: Consider the parametric curve defined by x=3+5t and y=1+31 Over which values of , does the curve has…

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Q: |x= 8| f (x) = Evaluate the left-hand limit of as X8. 16- 2x O 1/2

A: Given,            fx=x-816-2x as x→8To find : Evaluate the left-hand limit of the given function.

Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

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Q: 8:44 C ing e Determine whether the series is convergent or divergent. 00 1 n = 1 The series is a…

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Q: Example Evaluate +f -P) dpdgdr (p2 + q² – r²) dp dq dr + pq² – pr2 dq dr 3 1 + q? ² – r? } dqdr 3 -…

A: Let's find.

Q: Evaluate triple integral , S S dz dy dx. 4-y -2 Jx2 Jo

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Q: Choose the suitable function y1, for the method of reduction of order, to find a second solution y2…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = V9x2 + 16

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Q: Question 9 In Sx²/25+ x²dx , we let x= 5sine. (A) True (B) False

A: If x=5sinθdifferentiating On both sides.dx=5cosθ∫x225+x2dx=∫(5sinθ)225+(5sinθ)25cosθ…

Q: prevents changes to this answer. Which series converge in the interval described by x<1? 1.…

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Q: Cha invests Php5,000 in an investment that earns 5% per annum. How many complete years does it take…

A: The given problem is solved below in detail.

Q: 12x 3 3 15 12 x4

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Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

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Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: 3 5 8x 15 dx 5 x4 |

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

A: Here we have to use the trigonometric subsitution method.