At what interval is y=2x4-4x2 concave upward? 3 < x< 3 3 U x> 3 3. V V V

Q: Integrate f(x,y) = x + y over the curve C: x2 + y? = 9 in the first quadrant from (3,0) to (0,3).

A:

Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

A:

Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

Q: Find the function y(x) satisfying dx2 = 12 - 12x, y'(0) = 5, and y(0) = 8. ay = 12- 12x, y'(0) = 5,…

A: an initial value problem  is an ordinary differential equation together with an initial condition…

Q: Use the linear approximation to f(x,y) = x+6 at (4, 3) to estimate 10.1 y+2 4.9 10.1 V 4.9 help…

A:

Q: At what interval is y=x^3-3/2x^2 concave upward?

A:

Q: 10. Find the length of the curve y = x/2 + 8 on the interval [0, 2]

A:

Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

A:

Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0) = 0. Find its maximal interval of existence %3D

A:

Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: 2) f(x, y) = x +y on the closed triangular plate bounded by the lines x 0, y= 0, y+2x = 2 in the…

A:

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

A:

Q: S(x,y) =-x' +2x*y-² -4y+12 ED CALC

A:

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: express in the form y = f (x) by eliminating the parameter x = t + 3, y = 4t

A: The given parameters are x=t+3, y=4t. The objective is to express in the form y=fx by eliminating…

Q: Given y=[cube rt]x, find the local linear approximation for y near x=-8 and use it to estimate the…

A: Given: The function y=x3 To find: The local linear approximation for y near x=-8 and using this…

Q: at what interval is  y=3x^5-5x^3 concave upward?

A: Given y=3x5-5x3

Q: The distance from a point (2, y) to a line x – 2y + 3 = 0 equal to v5. Find the value of

A:

Q: Find the extrema points of f(x,y) =x3+6x2+3y2-

A: Given, fx,y=x3+6x2+3y2-12xy+9x Partially differentiate fx,y with respect to x: fx=∂f∂x=3x2+12x-12y+9…

Q: Integrate f(x, y) = y(x² + y°)° over the domain æ? + y? 0.

A:

Q: y = VT, y = 2 - x and r O about the x-axis?

A:

Q: Find fyry. f (x, y) - = x"y" – 9x°y + x f yry %3D

A: Partial derivatives are calculated with respect to y then x and again with respect to y.

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

A:

Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: Let z be a constant. Find the y" if y = v1 + 2zt + 5z't

A: Let z be a constant  To find y''if y=1+2zt+5z2t3

Q: find the value of c that the line y=3/2x+6 is tangent to y=c(sqr-root x)  c=

A:

Q: 2 5. x = 1+t2 2 y= t(1+t?)

A:

Q: What is the I.F of (x^2+y^2+1)dx+x(x-2y)dy=0

A:

Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

A:

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

A:

Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

A:

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

A:

Q: స్థాగ The length of the curve y = Ex3/2 between x = 0 and x = 1 is %3D 2/3

A: Length of the curve=∫ab1+f'(x)2dxy=f(x)=23x32f'(x)=23×32x12=xf'(x)=xLenth of the curve between x=0…

Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

A:

Q: а. max f (x, y) %3D 4x + 3ху + у S. t. х+4y— 29 3D 0 х+ 4у — 29 — 0

A:

Q: √√√(-) True f(x,y) dx dy False - L.T. 1.². f(x, y) dy dr

A:

Q: Find the interval on which the curve (x) = J di is concave downward. 6+ 8t

A:

Q: If u(x.y) and v(x.y) are differentiable, than, is it necessary that f(z)=u(xy)+iv(x.y) is also…

A: We know complex numbers are of the form ,  z = x + i y. Here , x = Real part of complex number  and…

Q: valuate dy and A v for v = f(y) = x2 -6x +35 x =4 and dy = Ax= 05

A:

Q: At what interval is y=2r4- 4x2 concave upward? U x> 3 x 3 3 <x<- 3 3

A: The given function is y=2 x4-4 x2 We have to find the interval at which the function is concave…

Q: If f=(3x?-3yz)i +(3y² – 3xz)j+(3z² – 3xy )K, then the value of the integral (f.dī along the curve x2…

A:

Q: On what interval is the curve t2 dt t2 +t+2 y = concave downward?

A: The given curve is: y=∫0xt2t2+t+2dt Using fundamental theorem of Calculus says: ddx∫axf(t)dt=f(x)…

Q: Find the length of the curve y =1+6x?on the interval 0<x<1.

A:

Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

A:

Q: 10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

A:

Q: find the extrema for f(x,y)= x^3 +y^3 -6xy

A:

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t