Find the indefinite integral. Solution in handwritten. 6x² 1. Sa -dx (4x3-9)3

Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: Given the general solution for a system X' = AX, X=C 2 + C2 e and 2 find the value of Ci & C2. 4 the…

A: Given;  X'=AX X(0)=(2            4).

Q: The average monthly precipitation P (in inches) for a certain city can be modeled by P = 1.81…

A: We need to find average precipitation.

Q: Evaluate the indefinite integral given below. ∫ x(x+7)4 dx

A: Given query is to find the integration.

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Given the query is to find the point of diminishing returns.

Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

A: This is a problem of vectors and integration. Based on concepts and formula of arc length we will…

Q: If f(x)=3+3x−5x^2 find f′ (-3).

A: Solution: f(x)=3+3x−5x2

Q: 5x-10 Find the area under the curve of f(x)=- 05 O-10In 2 O 5-10lm 2 0-5 from 1 to 2.

A: Solve the given

Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: 4) A degree 3 polynomial function, P(x) has zeros x 2, x = 1, x = m and a leading coefficient of 1.…

A: Here, the polynomial P(x) is of degree 3 and has three zeros x=2,1 & m and the leading…

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 6x + 17 between x =…

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Q: Solve me initial No need to Jimphiry. by value the separaion of variables a.

A: To solve the following initial value problems by the separation of variables.a y'=1+y2, y0=1b…

Q: Let f(x, y) = 6x cos (y). Find the conservative vector field F, which is the gradient of f. (Give…

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Q: Question 1: Find the Laplace transform of the given functions by using the table of Laplace…

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Q: y² − 5y = x³ - e² +c where c is the of integration. Setting x= we have . Thus, we have y — 5y — ( —…

A: This is a problem related to integration. Based on the general formula we will answer the question.

Q: Find the eccentricity of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. 2 1/2 2√7

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Q: Find the area that the curve encloses and then sketch it. r = 11(1 + cos ?)

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

Q: ICLO-3 Use the graph to ist() de.x) dx and S(x) dx in order, from smallest to largest 05 0 0.5 52 25…

A: Here, the curve is above the x-axis for [0,1] and the curve is below the x-axis for [1,2] &…

Q: Select the representations that do not change the location of the point a. [-2.-357) D. (-2,-²5) b.…

A: -2, 7π5=-2cos7π5, -2sin7π5π+2π5=7π5=2 cos2π5, 2cos2π5  [FIRST Quadrant]A)-2 cos3π5,…

Q: 47-48 Find equations of the tangent line and normal line to the curve at the given point. 47. y =…

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Q: Approximate the local minimum value of the function given below. Use Newton's method with the…

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Q: Use one of the following three formulas for the area of the region enclosed by C 1 fxdy = f - ydx =…

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Q: St-1.0t vemos anoitasu) InemzeozeA B C E M N K JH G Identify each of the following in the figure…

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Q: Find the curvature of the curve r(t) = (-4t, - 3t², 5+³) at the point t = − 2. Give your answer to 2…

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Q: The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x² - y² + 2z +…

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Q: 1) Calculate the following integrals. b) √₁6x²=1 -dx

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Q: the curve x=l-5¢, y=4€²-1 (0=ts) lengin find the arcC kngth of the curve x=1-. (ux calculator to…

A: This question is based on length of a parametric curve calculated using definite integral.

Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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Q: Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the…

A: According to the guidelines, we are instructed to answer 1 question or 3 sub question,the others can…

Q: The equation of motion of a particle is s = t³ - 27t, where s is measured in meters and t is in…

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Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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Q: Find all solutions in [0, 2π): 2 sin (x) - sin (2x) = 0: 4.8 00, π R/+ 4

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Q: Find the area of the region enclosed by one loop of the curve. r = 7 cos4e Select the correct…

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Q: A company selling baseball gloves has fixed costs of $1800, and it costs an additional $23.71 to…

A: This question is related to Cost and Revenue function, we will solve it using given information.

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: ∫0π22cos4xdx,  n=4Then ∆x=π2-04=π8The subintervals are 0,π8,π8,π4,π4,3π8,3π8,π2By midpoint…

Q: In order to solve with we first After where c is the y' we have - 3x² ex 2y - 5 the variables. This…

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Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 =

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Q: Weather condition Sunny Cloudy Rainy Snowy Percentage of days 42% 31% 18% 9% A) 1240 B) 3300 C) 2100…

A: Number of days in 2008 = 366 ( leap year ) Number of sunny days  =42%*366=0.42*366 Number of people…

Q: Find the area of the region enclosed by the inner loop of the curve. r = 2 + 4 sin ?

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: Solve the differential equation by separable variable

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

A: We have to convert the given equation.

Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y>0To find : Find the exact length of the curve.

Q: r(t) = cos(nt)i – In(t)j+ vt – 16k; to = 17 | -

A: Given :

Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: nd the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Given the query is to find the maximum profit.

Q: Problem 3. Solve 2+2 =10 4* +4 = 68

A: To solve the following system of equations.2x+2y=104x+4y=68