Consider the integral ¹ [ cot(0) · In(4 sin(0)) dº: This can be transformed into a basic integral by letting In (4 sin()). and U du do After perfroming the substitution, you obtain the integral du

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A: F = < 3x6y , xy3 + 7x7 >

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Q: If f'(x) = 2x O x² - In(x) O x² + 1 x² - In(1x1) O x² and f(-1) = 1, find f(x). In(x) + 1

A: Here we have a derivative f'(x). Need to integrate the derivative to find the function.

Q: nd the absolute maximum and absolute minimum values of f on the given interval. f(x) = In(x² + 5x +…

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Q: Use the information provided to write the standard form equation of the hyperbola. Show your work…

A: We need to find equation of hyperbola.

Q: Use L'Hôpital's rule 4. lim x csc x x→0

A: limx→0xcscx

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A: 1. volume of open-top cylindrical tank V=2000 cu meter 2. Cost of steel used for top and bottom is…

Q: Find the max/min / or saddle point of ', '

A: To find out the maximum, minimum or saddle point.

Q: 10e⁰.³x = 15

A: 10e0.3x=15formula used(i)  lnxn=nlnx(ii)  lne=1

Q: Exponential Sales Growth The sales of the Garland Corporation are projected to grow exponentially…

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Q: /0 5 5 8 For the matrix A = 4 5 2 19 4 4/ A. -7 C. - 12 cofactor C₂1? B. 12 D. 7

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Q: Multiply and write the answer in the form of a + bi (3-2)(3+2)

A: Given;

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A: To solve the following problem

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Q: Find f. f ''(x) = 4 + 6x + 24x2,    f(0) = 5,    f (1) = 14

A: To find out the function f whose double derivative and some initial conditions are given.

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: Given that f(x) = 4x2 and g(x) = 6 - x², calculate (a) f(g(0))- (b) g(f(0))-

A: The composition of the function f(x) and g(x) are: f(g(x)) and g(f(x))

Q: Q₁) Use Taylor's series method to solve the following differential equations (iii) y'=x+y²; y(0) =…

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Q: Exact Differentail Equation M (x,y) dx + N (x,y) dy = 0 is an Exact DE when ∂M/∂y = ∂N/∂x Solution…

A: (y exy - 2y3 ) dx + ( x exy - 6xy2 - 2y) dy = 0

Q: Initial Investment $1,000 5 Annual % Rate X% Time to Double 15 yr Amount After 12 Years $ 1740.87

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Q: A B C 50 560 610 R(t) 640 50- 40 30+ 20+ 10+ During a five-kilometer road race, runners pass a…

A: Simoly find the area under the curve to get the total number of runners.

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Q: Use L'Hôpital's rule 3. x³ - 1 lim x1 x³ + 3x - 4 3

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Q: Use the graph below to find the inflection point(s) and concavity: 5+ 10 -9 -8 Concave up: LD…

A: A graph of the function is given, we have to find the concavity intervals and the relative minimum.

Q: Given the differential equation: dy = tan y tan x. What is the general solution? Hint: Use…

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Q: Consider the equation   y=4x-x^2  on the interval [1, 5] a. Find all critical points (including the…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: A cylindrical can is to be constructed to hold 600 cubic centimeters of soup. The material for the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Your computer informs you that this gas follows the Ideal Gas Law (PV = nRT), and that the units for…

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Q: Use the given transformation to evaluate the integral. JJ² 2 sin(81x² + 81y2) dA, where R is the…

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Q: Find the solution to the following differential equation x²y" + 2xy' - 12y = 0 What is the form of…

A: x2y''+2xy'-12y=0

Q: 26. What is b if (log₁x) b = 1 -? 3x

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Q: particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 9, s(0)…

A: We have acceleration function. To find the position function, we need to integrate the acceleration…

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. lim n-00 00…

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Q: The first derivative of f(x) = = 10x³ - 3 (5x4 - 6x)³ C. (3-10x³)√(5x4 - 6x)³ A. Select one: O A OB…

A: Given a function f(x) , need to find derivative of the function. We will use chain rule to find the…

Q: xe-ye² = 0

A: Given expression xey - yex = 0  We can use the concept of implicit differentiation

Q: Consider the equation y=x^3-16x^2+2x-4 a. Determine all intervals over which the graph is concave…

A: For a function y = f( x ) For concave up f''( x ) > 0 For concave down f''( x ) < 0  Given…

Q: Find the volume of the figured form by rotation f(x) = 1 + 2x^2 around the line y = 5 on the…

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Q: lim X→0 2 (1— e(R+1)x) ²³ 1- cos X

A: To evaluate the following limit. limx→0 1-eR+1x21-cos x

Q: Find the value of f(7) when 7 1 cost - 2 sin 3 3 f'(t) = and f (1) (7) = 6. 2 3

A: f'(t)=73cos(13t)-2sin(23t)given  f(π2)=6

Q: Find the exact value of each expression, if it is defined. (If an answer is undefined, enter…

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Q: Consider the following graph. y 5 3 2 1 3456 (a) Find the interval(s) on which f is increasing.…

A: The graph of function f is shown as The function f increases in the interval where value of y…

Q: Clearly show all work. Use the graphs of x = x(t) and y = y(t) to sketch the parametric curve x =…

A: Given :      Aim:  To sketch a parametric curve x=x(t) & y=y(t) using the given curves.…

Q: Compute the volume of the solid bounded by the graph z = x² + y, the rectangle R = [0, 1] × [1, 5],…

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Q: The function p(t)- 20 sin 2xt + 100 models a person's blood pressure while resting, where p(t)…

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Q: 25. (Singular Value Decomposition) Suppose A = UDVT 3where U and V are nxn matrices with the…

A: To show that A is invertible, we need to show that its determinant is nonzero: det(A) = det(UDV^T) =…

Q: 8. State the intervals over which f(x) = x¹ + x³-2x² +4 is concave up or concave down and find any…

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Q: Suppose f(x) = = x + 1 I T 2 f(x) x+1 x - 2 x < -1 Complete the table Positive Negative Zero O…

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Q: Car north = x miles , car east =x+4 miles. distance btw both = 20 miles

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