DO NOT include spaces in between characters. * Using implicit differentiation, find the slope of the tangent line at the point (9,16) on the curve x + Vy =7.

Q: Q1: Find the integration of : (choose 3 only ) 1. Sc (3 sin x)cos (4 sin x). cosxdx Cos

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Q: Q5) Find volume of body bounded by z? + y? + x? = 9.

A: Let's find.

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

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: (x-2)" En=0 n2+1 n3D0

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Q: 22 – 9x? = 1 4.

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

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Q: Je* cos (7e*) cos (4e*)dx Evaluate: @ --co (3e*) -cos (11e') + C (3e*) – -cos (11e*) +c A 6. 22 ®…

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Q: Let r(t) = (t', 1- t, 4t). Calculate the derivative of r(t) - a(t) at t= 4, assuming that a(4) = (9,…

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Q: Consider the following function and dosed interval. fx) = x2/3 - 1, [-27, 27] Is f continuous on the…

A: F(x) is not differentiable on (-27, 27)

Q: The graph of a function f is shown below. YA f a Graph b 1. Which grap is an antiderivative of f?

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Q: Find volume of body bounded by z 0 from below and z = 4 - y from above inside y = x2 ,y = 4 .

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Q: J1 (3x -1)3 * tvt2 +1 dt

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Q: Evaluate +V7dx 3 Oa.5 +C 2 5 3. Ob.2 3 2 Oc 2 sm +- Ot ast Od +C 3 2 52~

A: Evaluate integral

Q: 1 Find f'(-1) if Ax) = (2x + 1)², O-4 04 O-1

A: The given function,       fx=12x+12

Q: Solve for "z" 7x + 3y + 8z = 10 -8x + 1y - 5z = 18 1x - 8y + 2z = 16 Round answer to 2 decimal…

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Q: cos x sin'x dx can be evaluated by factoring sin'x as (sin?x)²sinx and transform sin?x into 1– cos²x…

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Q: Consider the region bounded by the curve v= x2 – 1 and the x - axis over the interval [0,3]. Find…

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Q: Find the value of e which is defined as the angle between j+k and i+j_ None of the choices 4 프2 프3

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Q: Problem 2: Use the First Fundamental Theorem of Calculus to answer the ff. If F(x) = tvt +1 dt,…

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Q: 1. S(5x4 + 2x – 1)dx

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Q: "u,V.w are three vectors such that each is incined at an angle of 4 with the other two, and that lul…

A: To find the scalar product of two vectors with the given conditions.

Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

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Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y = T9x2 + 16 %3D

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Q: y = Vx* 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: There are 150 students in the marching band, and 30 of them play the trumpet. Which number line…

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Q: If u,v,w are three vectors such that each is inclined at an angle of 4 with the other two, and that…

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Q: Evaluate (s 2 ds Oa.2 sln2-1) (In2)2

A: ∫ s· 2sds=2ssln2-∫2sln2ds=2ssln2-2sln22Add a constant to the solution=2ssln2-2sln22+C

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: Q2) Solve the D.E dy - (2x/1– y²)dx = 0

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Q: Q1) Evaluate the following integral using Partial Fractions Method: y = : x³ +x? dx х2 +x — 2

A: Given: y=∫x3+x2x2+x-2dx   We know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: Q1) Evaluate the following integral using Partial Fractions Method: x3 + x? dx х2 + х — 2 y I|

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Q: sec'x tan?x dx, can be evaluated by using trigonometric transformation. A) True B) False

A: Let's find.

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

A: Topic = Area Area bounded by curves is 13.

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

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

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Q: The triangle ABC is defined by the vertices A(1, -2, 2), B(1, 4, 0) and C(-4, 1, 1). Let M be the…

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Q: 12x 3 3 15 12 x4

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Q: Each of the following limits represents a derivative f'(a). (5 + h) - 125 (a) lim Choose the correct…

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Q: Question 5. Find the Laplace transform of the following function by using the integral definition of…

A: Given problem:-

Q: Please answer the question below: Explain in detail which test you are using to determine…

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Q: Q3) Evaluate triple integral , dz dy dx.

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Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

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Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

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Q: EValuate J s 2'as O a. 2*(sln2 – 1) (In2)2 O b.2(sln2 - 1) (In2)2 O C. 25 sp.7s (1 – Zu). + 1) In2 O…

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Q: Find the derivative of f(x)= (In x O a. 6x(In x) O b. 24(In xỷ c. 24 In x O d. 12(In x)

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Q: Question For the function f(x) given below, where x > 0, evaluate lim f(x). X00 f(x) = In(5x² – 5) –…

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin (* + 0) in…

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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: Q2) Convert the polar function r = tan20 to cartesian

A: We know that x = rcosθ, y=rsinθ Given: r=tan2θ