5. Find the general equation of the circle of curvature of the parametric equation X= ;y=+√6(t+1); at y = 6 t+1 2 Equation of the circle of curvature:

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

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A: This is a problem related to partial differential method. Based on the general formula and concept…

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A: We have to solve integration

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A: Given

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A: First we rewrite the profit function in terms of t.Then differentiate p(t) with respect to t.

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A: Given query is to find the value of the integral.

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A: This is a problem related to integration. Based on the general formula and concept we will evaluate…

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A:

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A:

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A: answer is in next step

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We know that Critical points are points where the function is defined and its derivative is zero or…

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A: Using formula of d/dx(U/V)

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A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 e* cos (yz),…

A: We can solve this as follows:

Q: Solve the system of differential equations. X1' = 3x1 1x2 x₂ = 1x₁ + 5x₂ = - 11, x₂(0) = 7 x₁ (0) x₁…

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

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A: Solved below.

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A:

Q: f cot x dx Select one: a. In sina+c + c + c + c O b. In sec x oc. In csc r od. In cos x

A: cotx = cosx/sinx

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A: This question is related to cost and price functions, we will solve it using given information.

Q: 3 If f *¸9 (2) dx = -5 g(x) dx = -2 and Find the value of 3 15 -5 g(x) dx 15 g(x) dx = 9

A: Solution of given question is written in below steps.

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A:

Q: 1) Find a power series representation for the function and determine the interval of convergence.…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Solution: y=ln9-x2 Differentiate both sides

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Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We need to find critical point and graph.

Q: PROBLEM 5: Find the first three terms in each linearly independent series solutions (unless the…

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Q: Evaluate cos(x) - 1| dx.

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A: The given differential equation,D5+D4-7D3-11D2-8D-12y=0

Q: f cos √2x dx

A:

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Q: 7. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area…

A: Given