Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the line y = -2.

Q: Find the surface area if C = {(x, y): 1 ≤ x ≤ 2,y = about the x-axis.

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Q: What integration technique can be used to integrate: Integration Formulas O Trigonometric…

A: Technique used for integrating sec3x

Q: A bucket is filled with sand so that the total mass (sand and bucket) is 15 kgs. The bucket is to be…

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Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: e2-s L-1 (5(5²-53) O [(-1/3) + e^(4(t-1))/3] e^2 U(t-1) O [(-1/3) + e^(3(t-1))/3] e^2 U(t-1) O None…

A: We have to find the inverse Laplace transform of the above expression.

Q: What integration technique can be used to integrate: Integration Formulas O Trigonometric…

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Q: √√7 - t³, cos t³) t³, c 3 R(t) = (sin t³,-

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Q: 1+coshxsinhx+(sinhx)2 It is true that cosh x = Select one: True False Using Increasing/Decreasing…

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Q: Find the slope of the tangent line to the graphof the polar equation 1 TU r = at Ø 1-sino 6

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Q: True or false 1. √2 If cosh x = V, then sinh x = 2. It is possible for a function to have an…

A: Here we have to determine whether the statement is true or false.

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

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Q: (b) p = 2 sin p cos 0

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Q: If an investment grew to $13,500 in 3 years and the interest amount earned was $1,531.34, calculate…

A: To find out the compound interest.

Q: 7 x = R¹, ƒ(x):=· + 3√x² 1-x 1+x² +ea² +1 +π².

A: see below the answer and calculation

Q: Consider the vector-valued function R(t) = (t³ — t, 2t²,2 — 21.²). 1. Find ||'(t) || (Simplify your…

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

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Q: 4. f(x) = 4x cosh 3x x² ; f'(2.7)

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Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

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Q: 7. Use Disk Method to find the volume of the solid generated by revolving the R bounded by y =√x =…

A: Given that Region bounded by y=1x+1,x=0,y=4Revolving about x axisUsing washer/disk mathod…

Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim x-0…

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Q: Consider a right triangle with a side of length a opposite angle A. a side of length y opposite…

A: Given:  A triangle ABC right angled at C sinB=13

Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: projectile motion

Q: Find (a) v xw, (b) wxv, (c) vxv, and (d) wxw. v = i + 3j, w = 2i + 2j + 3k (a) v xw= (Type your…

A: Given query is to find indicated vector operation.

Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: Which of the following is not true? 5 C dx dx Ⓒ Im √² 250x² A S lim o 25-x² o c-5- ₂3 3 dx dx (B) √₂…

A: We have to find the solution

Q: 2x²+x-2 (x + 1) (x²+1) dx = √ [+41 + x+ 2 If S A B 5 © €/ 5 D 4 E) None 5/2 B (2x) + C 1 x²+1 dx,…

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Q: The curve y = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surfac area.

A: Here we have to find the surface area.

Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

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Q: [xv x√2x + 1 dx

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Q: 18. What is the length of the polar curve below? 3πt x = 8cos (0) for 0 ≤ 0 ≤ ³1

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Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Given than f(x) f²f(x) dx = −4 and Ⓒ [ƒ (2) de- f (x) dx = 20 (A) f dx [ B [²] ƒ (x) dx − [ª* ³ƒ (x)…

A: To find out the option which is not correct.

Q: II. Find the sum of the following convergent series. lim = = = lim lim 0-2 1 [tan ² (2n-1) - tan²¹…

A: Given problem:-

Q: The population of a city is modeled by the equation P(t) = 357,512e0.25(t) where t is measured in…

A: We have to find how many years will it take for the population to reach one million.

Q: 1. Given: parametric curve H defined by r(t) = tan-¹ t and y(t) = e¹, where t € R (a) Find the slope…

A: Solved below.

Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: Q1: convert the the Integral - (x² + y²)dydx to

A: Use the relation between cartesian coordinates and polar coordinates

Q: Given than han [ 1 (2) de = (z) dz=-4 and ® [1(e) de - [5 (2) de = 20 None of the given choices…

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Q: 6. Where does the normal line to the curve y = x - x² at the point (1, 0) intersect the curve a…

A: Topic = Functions

Q: Find the length of the spiraling polar curve r = 6e50 From 0 to 2. The length is

A: SOLUTION-

Q: dy Find the complete solution of 2e2¹ cosx- dx Note: [e"du=e" + C - sin² x = 0.

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Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

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Q: Which of the following is not true? Ⓒ √ 4dx √x(x+6) c lim dx ⒸS₁² 25² + x² ² m 25-x2 B dx c-5-0…

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Q: Trapezoidal method √√x dx for n = 4 is equal to Blank 1 (use 2 decimal places with proper rounding…

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Q: Using Simpson's method √x³dx for n = 4 is equal to 4.00 (use 2 decimal places with proper rounding…

A: Given,  ∫02x3dx, n=4

Q: Let x = 11t², y = 9t6 - 2t². d²y Determine as a function of t, then find the concavity to the…

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Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

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Q: Why did you take f'(x)=0 and from them I didn't understand, can you explain it a bit, its really…

A: We have to explain the term f'(x)=0.

Q: If fx √1- x4 dx = ge ½ A B 0 C D) 1 H|2 H|4 g(e) de, then 9

A: We can solve the given integral by using substitution.

Q: Convert the Cartesian coordinate (-1,-3) to polar coordinates, 0≤ 0 0 r = 0 =

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