9. For F = (x siny, tan(xz),ye¯²), find rot F. A. (-x sec?(xz) - e-zy-1,0, z sec²(xz) – x cos y) B. (0,0, 0) c. (x sec²(xz) + e¯*zy==-1,0, – z sec²(xz) – x cos y) D. (-x sec?(xz) – e-², 0, z sec? (xz) – x cos y)

Q: Find dwl dt at the given value for the following functions 1) w=x+y, x= cos(?), y = sin(t), at t = 7…

A: We have to use properties of trigonometric functions.

Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: Find Vf at the given point. f(x, y, z) = 32³ – 2(x² + y²) z + tan '(4xz), (0, 2, 3) Vf\(0,2,3) f(x,…

A:

Q: Find Wr 0 if W = f(x,y) x=r cos 0 and y = r sin 0, then prove that r Wr 0 =yfx + xfy + xy(fyy-fxx) +…

A:

Q: By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x…

A:

Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Find and by implicit differentiation, and confirm that the - dy results obtained agree with those…

A: The solution is as follows

Q: . Verify that u(x, y) = xy+7x +e° onjugates v(x, y) and find an expression for f(2) = f(x+iy) = u(x,…

A:

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: For F = (x sin y, tan(xz), ye-²), find rot F. A. (-x sec?(xz) – e²zy¯-1,0, z sec²(xz) – x cos y) В.…

A:

Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: Find əzləx of z = tan-1(x²y) + tan¬1(xy2). v² dz dx 1+x*y?° 1+x*y* ху 4,2 2,,4 dz 2ху 2y? Əx "…

A:

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: 2 The tangent plane to the graph of the function ƒ : R² → R defined by f(x, y) = −1+ cos(xy) +…

A:

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

A:

Q: af du (a) f(x, y) = sin-¹ (b) f(x, y): = x+y (c) f(x, y) = In ( t = 1 and u = 2 af and where Ət 2.…

A:

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: 1) F(x, y, 2) = 3xyi + 2yz j+ 7xz k. 3) F(x, y, z) = 6 e" senyi + 2e* cos yj + 9z k. 5) F(x, y, z) =…

A: We will find out the required value .

Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

A:

Q: -s Jatx? 3. 4-/ sinx coss dx |

A:

Q: 1 ezt dz 2ni Izl=2 z2+1 cos (t) o tan (t) o sec (t) o sin(t) o

A: See the attachment

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

A:

Q: Linearizations for Three VariablesFind the linearizations L(x, y, z) of the functions in Exercises…

A:

Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

Q: 4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z)…

A: Note:  Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Let v(x, y) = cos(4x) sinh(4y). Find f(2)with Im(f(z)) = v(x, y).

A:

Q: 2f sen jz įdz -2 cos z + C 28. sen Jz dz = %3D

A:

Q: sin(xz – 1) In(6+ 3xz + 4yz) = 0 determines z as function of x and y in a neighbourhood of the point…

A: Claim: at (x,y)=(1,1) for the equation  Take partial derivative with respect to x Substitute…

Q: дz in terms of r and t using chain rule if given that z=√√√4x² - y²₁ 1) Find and simplify dt x=r…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Let v(x, y) = cos(4x) sinh(4y). Find f(z)with Im(f(z)) =v(x, y).

A:

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: Given, y = cos2x We have to find dy/dt when x=π/4, given dx/dt=−4 when x=π/4.

Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

A:

Q: 1- Find dB/dx for the follow ing functi'on a)- xy = Cot (xy) b- y Sim(hs =-メy %3D c)- y?cos () 2x+2y…

A:

Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y).

A: using CR equation we get....

Q: Give the function z f(x, y)=4x²+ 3y, x(t)=sin tand y (t)= cos t. zp =2sin t.cos t 2.1 Show that dt…

A: The derivative of the function can be calculated by differentiating the function with respect to the…

Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

A:

Q: Find the following derivatives by using Chain Rule. a) dz/dt, where z = x sin y, x = t², and y = 4t³…

A: Let   U = f(x,y,z)   then dUdt = ∂U∂x·dxdt + ∂U∂y·dydt + ∂U∂z·dzdt As per guidelines, we are…

Q: Find a potential function for F(x, y, z) = (y² cos z, 2xy cos z, –ry² sin z). %3D COS

A:

Q: Find f(x)

A: We have to find out

Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

A:

Q: implicitly dx

A: Solved below

Q: 2. Consider the PDE u -t ux+ tu =0_for - ∞ <x< ∞ and 0 <t< ∞ with u (0, x) = sine x. Determine u (t,…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.