(A) Find equations of the tangent and the normal lines to the curve x-4t-3, y-3t-6 at the corresponding to t-2. Also find att 2. dx (B) Find the area of one arch of the cycloid x=r(t-sint). y=r(1-cost); Ost≤2x

Q: Tutorial on 1. Find Let cos²t } -St f(t) dt dt 11 e - St Laplace Transforms Also D to fe S tcost

A: Concept: Using the formulas: L{tnf(t)}=(-1)ndnF(s)dsn................(where…

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A: Since you have asked to solve two sub questions we will solve it.

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Q: Q1. 02. Evaluate the improper integral: 8 1 Se x(lnx)³ dx Evaluate the integral by integration b

A: As per bartleby guidelines we only give first question answers.

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A: This question can be solved using the concept of rate of change.

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Q: urrent Attempt in Progress Determine whether the homogeneous system has nontrivial solutions by…

A: See the answer below

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A: 1.] Given f(x,y) = √(y-x) For domain √(≥0) So, (y-x)≥0 Or y≥x Domain = {(x,y): y ≥ x} The Output of…

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A: Solution

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Q: 4. [App/10] fo the relation f(x) == x² - 2x determine f¹(x), graph both f(x) & f¹(x) and state the…

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A: We always check continuity of function in its domain . Hence the given function is continuous on its…

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Q: Find the absolute maximum and absolute minimum values of z€

A: This question can be solved using the concept of absolute maximum and absolute minimum.

Q: 9. Itan tan-¹ √u √u du

A: Given∫tan-1udu

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A: We can solve this as follows:

Q: Determine whether the series converges using the Ratio test. The series IM8 k= &

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Q: cot t(²7) + cos (7) sec (7). DO NOT RATIONALIZE. sin (5) c

A: To solve the following, using exact values.sin5π4 cot2π3+cosπ3 sec7π6

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Q: 2/ using the integration test the series A n³+n $ Σn. divergent n=1 √√√²² +21² +2 A true 1 Error

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A: p(x) = ax2+bx+c passes through point (1,7) , (-1,13) and (2,7). So, Form three equation using, p(1)…

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A: Given problem:- solve dy/dx =0.2y , y(0) =-2

Q: discover the area of the region enclosed by the following functions.

A: The given two functions:y=4x-x2 and y=2x-3.We need to find the area between them.

Q: Verify by Differentiation

A: This question can be solved using the concept of differentiation of function of function.

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Q: B: Solve the following differential equation by Laplace: d²y + 2 + 5y = et sint dx €13 ,y(0) = 0,…

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Q: ,)= 2 . Determine the equation of the tangent to the curve where x=0. Oy=-1+x Oy=-x+1 Oy=1 O None of…

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Q: P(AB) P(A) 13- P(B/A)= P(A)=0 (a) (c) P(A) #0 on condition that P(A)= (b) (d) P(A)=1

A: We know that P(B/A)=P(A∩B)P(A)

Q: integration function -1 ₁ 2²√x+¹(xy + 1)dydx 817718418 20 20 40 20 not of above - A - B - C - D

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Q: Evaluate the given Laplace transform. Do not evaluate the convolution integral before transforming.…

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Q: g(x) = 2x √1+3x

A: SOLUTION-

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A: To find dw/dk for the given w

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A: required graph of the function is blue y=-3 green y=3 red y=2x-3 black x=0 (I have assumed that…

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