Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when needed. Domain is: Choose one Choose one NOTE: Enter " [, ] r(15) (, ] [, ) r(t) = cos(πt)i – ln(t)j + √t − 14k; to = 15 ms of i, j, and k.

Q: find the equation of the line that passes through the point (-1,3) and is parallel to the line…

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Q: Σ n=2 7 n(In(n))*

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Q: Given: y = cosh cosh (ex²)

A: Formulas:ddx cos hx =sin hxddx ex =exddx xn = n xn-1

Q: COS X 6. y = x What is the appropriate formula? dx Solution:

A: Given query is to find the derivative of the expression.

Q: The cos³dy is {A}-sin+sin³+C 3 3 3 4 {B} sin¹-sin³+ C 3 4 3 4y (C)-sin-sin³+C {D}sin+sin³+ C

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Q: y Given: xe² + In(x - y) = . Find dy/dx. dy 2x(x-y)-x¹+x -w) (20

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Q: Find a critical point tid b.) relative maximum value valve C.) Relative mini mom d.) inflection…

A: Note :-  Here Equation of g(x) = 2x2-9x2+27 =-7x2+27 Or g(x) =2x3 -9x2+27  So we solve this problem…

Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

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Q: A Cessna plane takes off from an airport at sea level and its altitude (in feet) at time t (in…

A: Given: ht=2000lnt+1 Rate of climb will be rate of change of height i.e. dhdt

Q: 1. Given the following matrices: A = 1 2 3 4] 24 6 8 1 3 5 7 -1 2 -3 4 a. [(AC)BT] - DT b. [(BD)…

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Q: Find d² y dx² for x³ + y³ = 2 43

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Q: Evaluate the iterated integral. [²1²₂(x² - y²) dy d dx

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Q: x²-3x - 7 √(x² + x + 2) (2x - 1) dx

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Q: 1. Find the derivatives of the following function (a) y=4²+2√² (b) y=++ 2x+3

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Q: Evaluate the following integrals. 2. √x*+5x³ x+5x³+20x+16 x(x²+4)² dx

A: The given integral is ∫x4+5x3+20x+16x(x2+4)2…

Q: ₁ x³ In x dx e 3

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

Q: 1. Evaluate JJ (2². R where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 2}. (2x + y) dA

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Q: 2. Find each indefinite integral CS Searned with (278x²) da eamscanner 2.5

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Q: How to determine whether the function is continuous or not at a given point x = a ? x ≤ 1 (3x5 - 1…

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Q: Find the volume of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

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Q: Activity 2: Solve each function below the letters and decode the unknown word in each number. Once…

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Q: The function given is the population change per year of bald eagles in America P'(t) = 0.21t²…

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Q: Use the One-to-One Property to solve the equation for x. - 2x 7 = 4 X =

A: we have to slove the above question and find the value of x

Q: This is the length of the major axis, not the minor axis.

A: Apologies for the inconvenience.   Given equation is: 7x2+y2=49 We write it in the form: x2a2+y2b2=1…

Q: Find the total length of the curve r = acos² 0. (A) 3.12a B) 6.89a 1.19a 5.52a

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Q: L=

A: Follow the procedure given below.

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A: Follow the procedure given below.

Q: Locate the absolute extrema of the function on the closed interval. (a) f(t) = ₂, [3,5] (b) f(x)=…

A: The given functions,a) ft=tt-2, 3,5b) fx=x3-12x, 0,4

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: #6

A: Topic:- application of integration

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: x²-3x - 7 2 (x² + x + 2)(2x - 1) dx

A: Simplifying the given integrand: x2-3x-7(x2+x+2)(2x-1)=x2-3x-72(x2+x+2)x-12

Q: The fx³5x dx is x²+2 {A} x − ² (x² + 2)² + C 5 {B} x + ²(x² + 2)² +C {C}-{In|x² {D}+In|x² +21+ C…

A: integration

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A: Given: r=6cos3θ

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ||ti + 1²3|| dt =

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Q: As shown in the figure below, Mai is standing 100 feet from the base of a leaning tree. The tree is…

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Q: 2. Given the matrix A below, Solve for A-¹ A = 12 1 2 1 -1 2432 4] 365 487 - -3 4

A: Given A=123424681357-12-34 We want to calculateA-1=1A

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: y=x√3-2x³

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Q: 2. Boyle's law for the expansion of gas is PV = C, where P is the pounds per square inch of…

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A: As per the guidelines I can solve only one question

Q: Find the length of the parabolic segment r= 6 1 + cos 0 The length is. (Type an exact answer, using…

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Q: a. f(x) = on [-1,4] 1²+2 b. f(x) = I√4-1² on [−1,2] c. f(x) = 2 sec r - tan r on [0,1]

A: At the  extremum of a function f(x), the first derivative is zero.

Q: Evaluate the iterated integral. - y² I. L (x + y) dx dy

A: Take integration

Q: y = (In x) x , find dy/dx. Oy y' = (In x)* (1 + ln x) O y' = (In x)*¹ [1 + x (ln x) (ln ln x)] O (E)…

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

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