dx V4-x? 2.

Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

A:

Q: Find an equation of the hyperbola having foci at (4, – 11) and (4, 11) and vertices at (4, -3) and…

A: the coordinates of the vertices are  (h , k±a)(4, -3), (4, 3)k+a=-3,…

Q: Consider a triangle ABC like the one below. Suppose that b= 33, a=48, and B=26°. (The figure is not…

A: Sine Laws : asin A=bsin B=csin C

Q: Find div F and curl F if F(x,y, z) = x2°i+ 4y°x²j+ 2z²yk. div F=|2° + 12 y? x² + 4 z y curl F= 2 z2…

A:

Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

A:

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A: We have to find maclaurian series

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not…

A:

Q: A force of 9 lb is required to hold a spring stretched 6 in. beyond its natural length. How much…

A:

Q: respect to x of/ /(3Vi-1) dt is 3x – 1 by the 2nd fundamental theorem of C The derivative with (A)…

A:

Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: ydy can best be evaluated by algebraic substitution. Vy-1 A True В False B

A:

Q: Evaluate the following definite integrals. 3. If f(x) = V19+f dt ,find f'(3).

A: We can solve as follows

Q: af(x, y) If f(x, y, z) = , then is equal to dz

A: Given,  f(x,y,z)=x-zy-z

Q: Evaluate the line integral | -ydx + xdy along the curve C : y? = 18x from (18, 18) to (0,0). NOTE:…

A:

Q: x* +x? 5. lim, +* e* +1 In x 6. lim, csc(6x) csc(2x) 7. lim 5x+ 2lnx 8. lim, X+3lnx 2Tan 'x-x 9.…

A:

Q: Determine the vector field of F. F(x, y) = 9i – 3j

A:

Q: Find an equation of the hyperbola having foci at (1, -7) and (1, 3) and vertices at (1, -5) and (1,…

A:

Q: Problem 8 Find the following indefinite integrals: (a) [3r°dr (b) S(3r® +9x² – 12r)dr (c) S(7x-1…

A: topic- indefinite integral ∫xndx=xn+1n+1+C

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A:

Q: 10 10 If f(x) dr = 17 and f(x) dr= 12, then f (x) dr =5 A True B False

A:

Q: 21 3x7 + 8x 5x

A: Given: y=3x7+8x5-215x

Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

A: Solve the following

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: A detailed solution is given below

Q: Find the series' interval of convergence and, within this interval, the sum of the series as a…

A:

Q: Sketch the region enclosed by y = 4x and y = 7x². Decide whether to inte with respect to x or y.…

A: we have to find the area of the region .

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds tot = 0. Q…

A:

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

A:

Q: C sin 2wcos 2wciwv

A:

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: The point P(4, 24) lies on the curve y = z + x +4. If Q is the point (x, x² + x + 4), find the slope…

A:

Q: 21 Given 3x7 +8x5 - , determine, y" O 630x4 + 480x² + 126 5x4 O 840x3 + 360x 504 - 504 O 2520x3 +…

A:

Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). 13 r(t) = 3 cos(3t)i+3 sin(3t)j + tk…

A:

Q: coso de by trigonometric substitution.

A: answer is in next step

Q: Solve the seperable differential equation 10yy' = x. Use the following initial condition: y(10) = 7.…

A:

Q: Question 3 Determine the derivative of ln(csc x) - cot x CSC I O csc x cot x

A:

Q: (- 1)"(x + 1)" n! Consider the series E n=0 (a) Find the series' radius and interval of convergence.…

A: We will use Ratio Test for convergence

Q: Which among the following is false for getting the derivative of an implicit function? O Another way…

A:

Q: Vx² -9 What trigonometric substitution should be used to evaluate ? x2 A x=3 sece В x=3 tane C) None…

A:

Q: y= In e+1

A:

Q: Find dy/dx. x = Vt y = 9-t dy dx

A: Here, x=t3y=9-t

Q: S Sec ta

A:

Q: (ar3+ bx2+ cx) dr =2b x2dx where a,b and c are constana A) True

A:

Q: Ty csc?y dy is equal to A у coly + | coty dy - Scony dy В у coty — Scory dy —у сoty- —у coty + coty…

A:

Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

A:

Q: In |V Vr+i-2 dt, if we let / Vr+1 - 2, then dt is equal to A 4x°dx None 2(x²+ 2)dx (4x³ + 2)dx E…

A:

Q: dy Given the equation below, find dæ - 51a" + 7a"y + y10 = - 43 dy 172 (15 – 1422y) 29. dæ Now, find…

A:

Q: Y – C(Y)-I(i)–G, =0 kY +L(i)– M20 =0 %3D

A: answer is in next step

Q: Find the particular solution determined by the given condition. f'(x) = x2/5 + x; f(1) = -6 f(x) = =…

A: We can find the particular solution as below.

Q: lim 2?e --00 1- cos(2x) im

A:

Q: dy onsider the differential equation dx y? ) Re-write the equation in terms of differentials: dy =…

A: Given query is to find the solution of the differential equation.