Find the surface area for the object obtained by rotating y = 7x + 2 about the x-axis over the interval [2,5].

Q: Without using a graphing utility, sketch the surface with equation x2 + y2 − z2 = 0.

A: Surface with the equation

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

A:

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Find the point on the line y = 8x + 7 that is closest to the origin. (Hint: the distance between two…

A:

Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: Convert to standard from and give the center and radius: x^2+ Y^2 - 2x +6y - 1=0

A: x-h2 +y-k2 =r2 (h , k) is centre and r is radius .

Q: Let y= - Find the intersection of these surfaces, Calculate the GB of wrt lex order x>4>2)

A:

Q: Find an equation for the surface obtained by rotating the curve  y = sqrt(x) about the x-axis.…

A: Given, y=f(x)=x

Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: the origin 2 2 S (1-10²1) ² dx -1 2

A:

Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…