Q17 It z = f(x, y) and z* - x² = x²y°z? * and dz Find:

Q: dz Use an appropriate form of the chain rule to find dt z = 9x10y%; x = t10, y = t6 Enter the answer…

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Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

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Q: Q7) If y = tant ,x = tan?t at t = -! Find by using Chain Rule dx

A: We have to find derivative

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: dz Jse an appropriate form of the chain rule to find dt z = 3x*yl0; x = tº, y = t7 Enter the answer…

A: Topic- Differentiation

Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: dy Find - xp x = t sin(t), y = t? + 4t

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Q: dg at t = 2 dt Given g (x, y) = x² + In (xy?}vhere a = t'and y = t³ Find

A: I am attaching image so that you understand each and every step.

Q: *f(x,y) = xy + aS lšl fry.fyx gl y²+1

A: Given fx,y=xy+eyy2+1

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/escx))

A: To find the y"+3y'×5y at x=5  Given y=xsin(1/cscx)

Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

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Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: Ost<4, find F(s)=L{f (t)} using the defintion. e #1.) Given f (t) = 1 , t24

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Q: Q/ For the function shown bellow; find dyldx using Chain rule Y = ( 4 2x + 4)*

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Q: Q2: Find Wx, Wyy, and Wxy for the function ху W = x sin(y) + y sin(x) + xy ||

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Q: Calculate the LOS of y = x² LOS is x = a is b is c is

A: Given equation is in the form of ax^2+bx+c=y Here a=1 b=0 C=0.

Q: E(x)三ㄧ-rx.VY.tmdt. Į nd Eicx) Let

A: Since f(t)=sqrt (4-t^2) is even function , so we use the property of definite integral shown on…

Q: Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

A: As per our guideline we are supposed to answer 3 sub parts of a question please repost the other…

Q: Evaluate f(y dx + x dy) around a closed curve C take taken counterclockwise. Select one: а. 1 b. 3…

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Q: Find for the following by using appropriate rules: dx i. y = Vt , x: X = t+1

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Q4.SuPPe that r=xy and x=Y Co1 8, asin Polur Coordinate dr dx Jy Find and

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Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: dx find . diven that x>0, using the substitution u =

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Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: Hn obfect Is moving along the X- axis with acceloration givon by at) =Q +42zt. TF V l0) =1 and…

A: Given query is to find the displacement function for the acceleration given.

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: V Sove using variaton of parameters recuction of order or (D² - 2D+1) y = e*(e*+)*

A: Please find attachment for the details solution

Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

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Q: Find fxx, fxy, fyx, and fyy if f(x, y) = sin²(x – 3y) %3D

A: f(x,y) = sin2(x - 3y) fx = 2sin(x - 3y)cos(x - 3y) fy = 2.(-3).sin(x - 3y)cos(x - 3y) = -6sin(x -…

Q: U (d) Let t ==; V at u = x² - y², v = 4xy³. Find- and Əx dy

A: According to our guideline we can only answer first question and rest can be reposted.

Q: dz Q2 Given z = xw? + cos y + wx , w =t, x = 2t2, and y = 3t, find dt

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Q: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

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Q: Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

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Q: dz Given z = 4x? + y²,x = sin t, y = t², find - dt

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Q: Let f(x, y) = /T²(1 – y²). Find fr (0, 1).

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Q: Find the 2nd solution using variation of parameter. y" + 16y=0; y₁ = cos4x For the toolbar, press…

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: Q2: Find Wx, Wyy, and Wxy for the function W = x sin(y) + y sin(x) + xy

A: We have to find partial derivatives of W.

Q: Q2 Given z = xw? + cos y + wx , w =t, x = 2t? , and y = 3t, find dt

A: Let's find.

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.