Find r(t) if r'(t) = t² i + et j + 3te³t k and r(0) = i + j + k.

Q: Evaluate the integral. 8y' dy 8 y 8y' dy 8 y - 4 - 4

A: Solving the problem by finding the value of the integration.

Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast (in cm²/sec)…

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Q: Find volume of the solid of the region between y = x^3 and y = x^2 for [0,1] when rotated around y…

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Q: dy The general first order linear equation can be written in the standard form dt The equation ty' +…

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Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x +110. Use the…

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Q: Use algebra to evaluate the limit. (1 + h)² − (1 − h)² 2h lim h→0 i |

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Q: If a = [5,-2,1] and b.= [-1,-3,4], find | -a + 2b |

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Q: i cant see the rest of the solution

A: To find the integration.

Q: Find Əf ax and for the following function. Əy f(x,y) = e³xy In (3y)

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Q: The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.…

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Q: Solve the initial value problem. d²y y = 2 dx = 4e x, y(0) = 2, y'(0) = 3

A: Here is the solution:

Q: The following figure shows the discharge rate r(t) of the Snoqualmie River near Carnation, Wash-…

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Q: Compute the volume of a solid obtained by rotating a region below the graph of y = -∞ < x < ∞0. (Use…

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Sol:- We can use the method of cylindrical shells to find the volume of the solid obtained by…

Q: 28 f. (7/₂) = x -J 12-x x-12 X+6 Olet fi R+R be defined as f(n)= 3√x + sinda and g: R-SR is defined…

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Q: Let A = 6.1 ag - 2.5ẩn and B = -2.9 ấg + 4ẩn given the unit vectors âg=0.60 +0.8ây and ân =0.8ân –…

A: GivenA→=6.1ag^-2.5ah^B→=-2.9ag^+4ah^ag^=0.6ax^+0.8ay^ah^=0.8ax^-0.6az^   We are required to…

Q: पी T [-3, 3] Graph of f b The graph of the function fabove consists of four semicircles.if g (2) = /…

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Q: Verify by substitution that the given function is a solution of the given differential equation.…

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Q: Find T and N for the space curve, where t> 0. r(t) = (9 cos t + 9t sin t)i + (9 sin t - 9t cos t)j +…

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Q: 16y²+z² = 25 2

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Q: Algebraically determine the following limits: lim+x-12 +3x²-5x+6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The graph of f(x)=-2x² + x²-2 is shown below. Use the tools to graph the line tangent to f(x)…

A: Given curve equation:- fx=-2x3+x2-2

Q: Given the points X (1,2,-1)  and  Y (0,3,-2), find a vector collinear with  XY  having opposite…

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Q: {} n+1 •n=1

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Q: If f(x) = sec x, find f"(π/6).

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: If the function is never increasing or decreasing, enter NA in the associated response area.…

A: Given query is to find the interval where function is increasing and decreasing.

Q: 3. Two forces F, and F₂ push on an object with an angle of 70° between them. If F=170N and the…

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Q: Maximize f(x, y, z) = 2x + 5y + 9z on the sphere x² + y² + z² = 55. 5√ 110 X

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Q: The vector r(t) is the position vector of a particle at time t. Find the angle between the velocity…

A: To find the angle.

Q: Consider the function f(x) = 3x²-x+5. 1. Set up, but do not evaluate, the limit that would compute…

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Q: Find the Maclaurin series for f(x) = What is the Maclaurin series of Σ n = 0 5 1 + x 5 1 + x (Type…

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Q: 3x-2 f (x) = 52−3 - show that the inverse function is of the same form 7. If

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Q: Evaluate limit lim [ln(x² + 3x + 1) − ln(x + x³)]. x→∞

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Q: (x + y)dx + (2x - y)dy = (

A: The given differential equation is x+ydx+(2x-y)dy=0

Q: A particular solution of y" + 2y' + 5y = e sinx

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Q: Problem #8: Consider the following matrix. 1 409 A = 1 1 1 Given that λ = 0 is an eigenvalue of A,…

A: We can solve this as follows:

Q: Need the answer to both questions asap

A: Answer to the first question  ***Figure 3 is matched

Q: Given f(x) = {² -7 6 X if 0 ≤ x ≤ b if b < x a) Determine a value of b so that the function given is…

A: Given:  fx=x2-7 if 0≤x≤b6x if b&lt;x To Find:  (a) To determine a value of b so that the given…

Q: K Find the unit tangent vector of the given curve. r(t) = 3t³i-12t³j+ 4t³ k 3 OA. T(t)= 1 13 3 OB.…

A: Option (B) is correct answer  For detail go through the solution I have solved step by step in…

Q: Find the Taylor series generated by f at x = a. 5 f(x) = a=1 2 X Choose the correct answer for the…

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Q: Find the angle (where 0° ≤ ≤ 180°) between the following vectors. Give your answer accurate to at…

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Q: The graph of y = 11 -10 -9 क =m (x) is given below. Answer each of the questions below -7 -6 -5 14…

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Q: Find the center and the radius of the sphere. x² + y² +z²-3x + 2z=0 The center of the sphere is (0…

A: The given equation of sphere is: x2+y2+z2-3x+2z=0 To find the center and the radius of the sphere.

Q: Starting with an initial value of ​P(0)=20​, the population of a prairie dog community grows at a…

A: Given query is to find the population after 13 months and the population function.

Q: Consider the curve f(x) = x - x³. (a) Find the slope of the tangent line to the curve at the point…

A: To find the slope and equation of tangent line.

Q: Find the volume of the solid obtained by revolving the region in the first quadrant bounded by y =…

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Q: Evaluate the integral. BeBy S 4+eBy dy

A: We can answer the given integral in the below steps.

Q: It did not accept 824.77 as the answer

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Q: The substitution best used in: da +x+³x is

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: NOTE: Refresh your page if you can't see any equations. .