. Solve the following problems using the concepts of Parametric Equations. Show complete solutions. 1. Find the equation of the tangent line (s) to the following set of parametric equations at the given point. a. x = 7sint and y = t2 + 1 at (0,3) b.x = evt and y = t – Int? at t = 1

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A: The given equation,    x3+x+4=0

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A: Explanation of the answer is as follows

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A: Given problem:-

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A: LetI=∫xx2-43dxPut x2-4=udifferentiate 2xdx=duxdx=du2I=∫xx2-43dx.I=∫u32duTake the constant out:…

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A: The given integral,                        ∫05ti+t2jdt

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A: This question can be solved using the concept of second order derivative.

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Q: 15. Indefinite Integrals (Part 1) а) -+ cscxcot x dx 2 cosx--sinx+4csc². 3 b) 1 + sec² x dx 1+x2 c)

A: topic - indefinite integral

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

Q: 2/ Find the value of the limit: lim x/*,

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Q: 1. Consider the curve defined by 9x2 – 16 y² +36x + 96y– 252 = 0. a) Write the equation of the curve…

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A: Given that, fx=4x-x2 We need to compute the value of f'a.

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Q: S csc2xdx cosx O sinx+C O -cotx+C O -cotx

A: By using standard formula.

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Q: Example: Find C² sint]? Solution:

A: To solve the following problem

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A: integration

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A: The given sequence,      1,32,56,724,9120,11720

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A: This is a problem of differentiation . Based on the formula and concept we will answer the question.

Q: 1-

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Q: Find a formula for the nth term of the sequence (choose one of 2) The sequence 2,6,10,14,18, ..

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: dx Va - x2 we may use x= and dx= substitutions to reduce the integral to San do. This step requires…

A: To complete the following statements.∫dxa2-x2we may use x=? and dx=?substitutions to reduce the…

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A: Given problem:- f(x)=(x-4) /(x2 +2x+17)    What monomial expression best estimates the behavior of…

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A: First I have used  a substitution and made integral easy and then solved it.This is the process.

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Q: Evaluate the definite integral. e14t i + e¬1j +t k )dt O el4 (e-- – 1) j + k i+ 14 (el4 – 1) i- (e -…

A: Evaluate the definite integral

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Q: Fill in the Venn Diagram below by dragging the appropriate entry to the orrect location given that:…

A: Explanation of the answer is as follows

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A: topic - application of derivatives

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Q: 2. For the parametric curve defined by: x(t) = t2 + 4t + 2 y(t) = t³ + 2t2 + 4t + 1 (a) determine…

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A: Here we have to check the convergence of the sequence.

Q: 75 then compute the limit. 137 2| %3D Investigate the one sided limits (left and right) of f () =…

A: Given query is to find the limit.