4. Consider the curve with equation y = x* as shown in the diagram. A tangent line meets the curve at the point A(a*, a"). A(a*,a") (a) Find the equation of the tangent line at A. (b) Find the area of the shaded region enclosed by the curve, the line y = 0, and the tangent line.

Q: 2) lim- x) Tanx

A: The given limit is              limx→π2π2-xTanx we know,     Tanx= sinxcosx

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A:

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A: car cost Php 800000 value after 4 year = ? per year depreciate is 20% 800000*20/100 = 160000…

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A: To find dydx& d2ydx2 using the given parametric equations.

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A:

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A:

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A: A detailed solution is given below.

Q: Question 1 Determine the inverrse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

A: L-11s-a =eat L-1as2+a2=sin(at) and L-1ss2+a2= cos(at).

Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 352+5s+1 (d)…

A: Let's find.

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A:

Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

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A:

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A:

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Q: Integrate sze" • fa". de Answer:

A: We have to find the integral

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A:

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Q: Convert to a rectangular coordinate. Convert to a polar coordinates. 5T 10. 11. (-4,4)

A:

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A: Find inverse Laplace

Q: Calculus How many numbers are relatively prime to the following number. - 209 - 323 - 867 - 31…

A:

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A: Given ,  A local diner must build a wheelchair ramp to provide handicap access to the restaurant.…

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A: The objective is to find the derivative and slope at the point .

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A:

Q: Show that - 8. ==1+* +4++++1=

A: We know ∑1n2=π26  Hence, ∑1(2n)2+∑1(2n+1)2=π26 Therefore, 14∑1n2+∑1(2n+1)2=π26 ∑1(2n+1)2=π26 - π224…

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A:

Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: A detailed solution is given below.

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A: Given f'(2)=5To find ddx[4fx-x3]x=2

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A:

Q: A. For each of the following functions z, find and dx ду 1. z= sin3x cos4y 2. z = tan- 1 (2) 3. yz +…

A: 1). Given: z=sin3xcos4y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x…

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A:

Q: a?z B. For each of the following functions z, find a2z and ду? a²z дх? дудх' дхду" 1. z = 2x2 – 5xy…

A:

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

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A: Given

Q: dr

A:

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A: You have asked multiple questions and not mentioned which question answer you need so according to…

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A: Given that the curve  r→t = 2 costi→ + 2 sintj→ +3tk→  = f(t)i→+g(t)j→+ h(t)k→        we  have to…

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A:

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A: .

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A:

Q: B. For each of the following functions z, find and dx²' dyðx' axðy' dy2 1. z = 2x² – 5xy + y²

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A:

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A: We have to convert an angle of 78°24'17" in degrees.    Before converting, let us see first two…