A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P in such a way that the area of the region bounded by this line and the parabola is square units. Determine the coordinates of P.

Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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

A: Given: Now,          F(1)=∫11tt+1dt=0. Here,               F'(x)=xx+1⇒F'(1)=2 Further,…

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

A: ∫-22∫x24∫04-ydz dy dx∫dz=zSubstitute the limits=4-y-0                              =4-y

Q: Given the function: f(x,y) = 4x*y² – 10p +y , find f a. 16x'y-60xy O b. 48x°y O C. 16xy – 10y O d.…

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Q: The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial…

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

A: Draw the graphs of the given curves and mark the intersection area.

Q: Differentiate Derivative of outer function  Derivative of inner function Differentiation  1. y = sin…

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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: Evaluate the following integral using Partial Fractions Method: x3 + x2 y = dx x² + x – 2

A: Let…

Q: 3 3 25x ? 2 7x3 3 16х5 dx 5

A: use property of integral to solve this.

Q: Problem 1: Evaluate the following definite integrals. Sx(x2 + 1)V4- 2x2 – x dx -dx

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Q: 2. S dx I+,x

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Q: +1

A: I have stated the used formula in the solution

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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Q: Descibe he moton of a partice with position y= 5 sin t; y=2 cos t as t varies in the interval - T, 5…

A: To find the motion of particle.

Q: Determine the slope of the tangent to the curve y – 3.xy +2x =4 at the point (3, 2).

A: curve :  y2-3xy+2x2=4differentiating w.r.t…

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

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

A: Topic = Integration

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: u+v+w=0ad u =3, v=5, w = 7 then he angle between y and y is 0 2r 6. 0 5m ONone of the choices 11

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Q: Find the total distance traveled by a body and the body's displacement for a body whose velocity is…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: QI) Evaluate the integral dx dy using polar coordinate

A: Solving

Q: *) dx Evaluate:

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Q: 1 et dx 1 (1 — е*)2

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Q: 1 dx x[9+(ln 3x)" 8.

A: use simple integration method.

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: Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two…

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Q: Evaluate triple integral , dz dy dx.

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: 22 – 9x? = 1 4.

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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: Let f(x) be the function 11a - 5x+4. Then the quotient f(8 + h) - f(8) can be simplified to ah + b…

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Q: Determine a and b so that the function f(x) is continuous for all values of x. jika x <- 2 sin x…

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Q: Find (a) if fx) = /x-a+1.

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

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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: Cara tosses a pair of equally weighted coins 4000 times, and two heads appear 40 times. What is the…

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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: Evaluate the following integral using three different orders of integration. SSL:(x: – y') dV, where…

A: Here we have to evaluate the given integral.

Q: 2x 4. Given the function F (x)= 3 do the following: 4.x +1 a. Find F-1 (x). b. Find dom F and dom…

A: Given,            The function is Fx=2x-34x+1.

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

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Evaluate f s 2°ds О а. 2"(sin2 - 1) (In2)2 O b. 2(sln2 - 1) (In2)2 O C. 2* In2 O d. 25 In2

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Q: 3 5 8x 15 dx 5 x4 |

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Q: Q2) Convert the polar function r tan20 to cartesian.

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

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Q: Q3) Evaluate triple integral f x - y²)dz dy dx.

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Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

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Q: sin7t sin4t dt =- 121 – cos 31) dt A) True B) False

A: