Evaluate the following: 6. Se (y, 1) - dr where r(t) = (t3 –t, 2t) from (0,0) to (6,4).

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: dw Use an appropriate form of the chain rule to find dt w = In(162? – 4y + 3z³); 1 = ti, y = tỉ,…

A: Topic- differentiation

Q: ds if s = In [t*(t² – 1)]| dt 20. Find

A:

Q: 3. y = 1+Vx eğrisi, y = 3 – x doğrusu ve eksenler arasında kalan bölgenin koordinat düzleminin 1.…

A: Given the curve y=1+x, and the line y=3-x. Find the area between the curve, line  and bounded by the…

Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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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: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: Q6. If w = y²z² + xy and x = t³ – 1; y=t² + 2; z= 3t , find the total dw at t = 2 dt differential

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Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3 , by using the Chain Rule dt

A:

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

A:

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

A:

Q: dy 3 4-1+2у, dt (0) = 1

A: Given dydt=4-t+2y   ; y(0)=1  with h=0.1

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

A:

Q: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

A:

Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: Given z = 15 In(t) and y =225 t then find dy da dy da?

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Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

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Q: dw Find if w = xy? + x²z+yz?, x = t², y = 2t, and z = 2. %3D dt |t=1

A: Simple derivative problem....

Q: Find dw/dt at t 1 if w xe + ysinz - cosz, r ! = 2/t, y = t – 1 and z = nt.

A: v

Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 2, and dz/dt = 2. (Enter your answers as a…

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Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

A:

Q: | Calculate the following antiderivatives: / 6r – 2° + 7 dt = [T (a) +C. (b) ul/4 1 + 6yū du = +C. 1…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: Find dy/dt if y is as follows. t2 + 4 y = In 7 - t dy dt II

A: We use logarithmic properties to simplify the given function and use chain rule to solve this…

Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: s zy dydz こミ0

A:

Q: at at 4) Let t = ,u = x² – y² ,v = 4xy³. Find· ay əx

A: To find: The value of ∂t∂x, ∂t∂y. Given information: t=uv, u=x2-y2 and v=4xy3 Concept used: Quotient…

Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

A:

Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

Q: dw Use chain rule to find dt if w = xez, x = t², y = 1- t, z = 1+ 2t.

A: Given w=xeyz, x=t2, y=1−t and z=1+2t We have to find dwdt by using chain rule. Hence, by chain rule…

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Given f(x, y) = - (4x°y + xy® ). Compute: dy?

A: