[3-x 2 2 2 4 - x -2 -4 -1 - x. 0,2 O 0,3 O 2,4 O 1,3 1,2 O

Q: Q2) Convert the polar functionr tan20 to cartesian.

A: Here we have to convert the polar function r=tan(2θ) to Cartesian.

Q: r= sin E-0) in first quarter.

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Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: The water is leaking at the rate of π/2 m³/min.

Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

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

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Q: 9. If f (x,y,z) = 3x²y – xyz + y²z? _Ifind each of the following: fy (x, y,z) C.

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

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Q: (3-y Q1) Evaluate the integral dx dy using polar coordinate

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Q: A rectangular piece of cardboard has a size of 45 x 24 cm. This cardboard will be made into a box…

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Q: a ) Σ-1 (-1)"-1 Zn=1 2n+1

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Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: sin x xý + 3y += x2

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Q: The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in…

A: Here, the volume is: V=∫03π(y)2dx =π∫03x2-2x+22dx=π∫03(x-1)2+12dx

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: 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…

Q: Find the derivative of f(x)= (Inx Oa 6x(Inx Ob. 4 inx Oc 12(in a Od 24(inx

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

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Q: (e) Suppose that the functionf is represented by the power series f (x) =1- +(-1)*. - -- +... 2 4 8.…

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Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

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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: dy Vy+2 sinnx costx dx

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Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: PART II. Find the derivatives of the following expression, solution must be presented. (3 marks…

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

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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: The limit represents a derivative f' (a). Determine f(x) and a. 14h lim 1 h→0 (Express numbers in…

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Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: 4. Estimate the net area under the curve bounded by the x-axis from x = 1 to x = 7 with 12…

A: answer is in next step

Q: Find f"(1) if fx) = x- 2x+ T. O 3n? - 2 O 31? – 1 12 - 21

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Q: Learning Competency: illustrate an antiderivative of a function. Question Is S Gx2 + 5x + C)dx = 3x…

A: Given,             Is ∫32x2+5x+Cdx=3x+5 correct.

Q: dy Find the general solution of 2x² = a? + y? dx %3D

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 9…

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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: 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: Type your answers in the following order and format: a=1,b=2. DO NOT include spaces in between…

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Q: 5. In antidifferentiation, the formula J x" dx : + Cis valid if? (n+1) C. ne {0,1,2} A. nER 6. In…

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Q: x- 2 For the function f(x) = x-5 a. the graph of the function is until x = 2 only. O b. the graph of…

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Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y V9x² + 16

A: The given integral is y=∫dx9x2+16 We have to solve the integral using Trigonometric substitutions…

Q: Consider Evaluate ( 3x² + 6x ) e *+2) (6x2+ 3x) e +y2) (6x+9x)e+y2) O (9x4+6x) e *+y2)

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Q: Q3) Evaluate triple integral f , (x2 -y²)dz dx dy.

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Q: Determine the equation of the tangent to the graph of y = [2~/x - x][1+ /x - x ] at the point (1,…

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Q: *) dx Evaluate:

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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: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

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

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Q: y = Vx* X

A: