Evaluate (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

Q: write the equation of a parabola whose directrix is x = 5.75 and has a focus at (12.25, 5).

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

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Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydr (8r+7)dudy O none of the oices

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Q: Show that the set of all points P that are twice as far from (-1,5,3) as from (6,2, –2) is a sphere.…

A: The set of all points P that are  twice as far from -1, 5, 3 as from 6, 2, -2. Let coordinate of a…

Q: Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O…

A: We need to find centroid of the region.

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: 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: 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: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x2 + 16

A: We will use simple Integration rules to solve this question.

Q: 4. S cot?x dx

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Q: Find the distance between the skew lines: x = 4+ 9t, x = 4 – t, y = 3+ 2t, z = 7 – 4t y = 9, z = 8+…

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Q: Find the volume trapped between the cone z = 2 – Vx² + y² (upper) and the paraboloid z = x² +y².…

A: We need to find volume.

Q: ) Oppositely directed to v = (15, –18) and half the length of v. w = (?, ?)

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Q: Determine the general equation of the plane Ω passing through the point P(−5,−4,1) and parallel to…

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

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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: (a).x = 61, y = - 4 + 7t O (r, y) = (0,4) + «(6, 7) ai + bj = 4j + 1(6i + 7j) O (1, y) = (6, 7) +…

A: topic - equation of a line

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: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Which of the following yields the value 3580? O none of the choices (18x+7y)dxdy (18x+7y)dydx…

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: Find an equation of the plane that passes through the point P(-5, –8,8) and has the vector n = (-8,…

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

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

A: Given,             ∫7x-1x2-2x-48dx

Q: 22 – 9x? = 1 4.

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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 h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

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Q: 4 r4-y Evaluate triple integral , S S dz dy dx -2

A: We have to evaluate the triple integral  ∫-22∫x24∫04-ydz dy dx.

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

A: Topic = Algebra

Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

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Q: 1 Find "(x) if Ax) -. %3D X+1. 1 (x+1) (x+ 1) -2 (x+ 1)3 12

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Q: Find the smallest number n of terms needed to obtain an approximation of the series 27ke-0.254² k=1…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (9, –5)…

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Q: Find f"(2) if Ax) %3D x² - 3* 08 O -7 4 O 2

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Q: For the functionf(x) given below, where x > 0, evaluate lim f(x). X00 f(x) = In(3x' – 3) – In(4x² +…

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

A: The given integral,       ∫excos7excos4exdx

Q: 18. Find the shaded area in the following figure. Assume that there are infinitely many squares and…

A: Area of Infinite shaded region Let Sk be the sum of area of each shaded regionthen…

Q: х2 — бх + 9 dx V6x – x2

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

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Q: Evaluate the following limit: x² + x- 2 lim- x-1x2- 2x + 1 If it does not exist enter DNE. Round to…

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Q: (a) Find the first partial derivatives of the function f(x, y) = x²yVy + 4y². %3D (b) Find the…

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Q: From Rogawski ET 2e section 10.3, exercise 10. Use the Integral Test to determine whether the…

A: Given problem:-

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

A: Let's find.

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

A: Let's find.

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Is Rolle's theorem valid for the function f(x) = Vi-x on the segment [-1,1]? a. No since the…

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