Evaluate the following integral: |sec2 (z) tan (z) dz = 因团 +C Be sure to enter powers of trigonometric functions by typing, for example, sin (x) ^3 for sin (x) (i.e., do not type sin ^ 3 (x)). Note that an arbitrary constant has been added for you.

Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

A:

Q: The answer above is NOT correct. Use calculus to find the volume of a cap of a sphere with height h…

A:

Q: Evaluate the line integral, where C is the given space curve. xyeY dy, C: x = 3t, y = 2t, z 4t,…

A: Here we have to find line integral.

Q: Solve the inequality involving absolute value. |x-3|/4<2

A: Given :        x-34&lt;2

Q: Find div F and curl F if F(x, y, z) = 7y°z*i – 11xz'j – 6xy°k. 5.7 div F= curl F=

A:

Q: ах 2xy 2.xy +3y x +2xy dy dx

A:

Q: 16. Find the volume of the region that lies under the graph of the paraboloid z = over the rectangle…

A: Here, to find the volume of the paraboloid z=x2+y2+2 over the rectangle R=(x,y)∈ℝ2|-1≤x≤2, 0≤y≤2

Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: Determine the vector field of F. F(x, y) 3D 6і — 2)

A: GIVEN :                  F(x,y) = 6i - 2j.           ------(i)  We have to determine the vector…

Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: To find dy/dx.

Q: Evaluate the iterated integral. 4ze dy dx dz

A:

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) j+…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Find V · (V × F) if F(x, y, z) = 4 sin xi + 8 cos(7x – 8y)j + zk. V: (V × F)

A:

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y3, P(4,…

A:

Q: Graph the eauation - include local+ Absolut extreme Points if applicable - -include inflection…

A: maxima minima

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

Q: Find the e v

A:

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

A:

Q: Clear denominators in the following partial fraction decomposition and determine the constant B. 3x?…

A:

Q: 3x?+4x-7 ii) lim x2+9 X00

A: Given query is to find the value of the limit.

Q: Describe the graph of the equation. r = 7 cos t i – 17 sin t j +k O An ellipse in the plane z = 1,…

A:

Q: Find the Taylor series centered at a = 0 for the following function: -7x f(x) = e 8. Answer: n=0 (Be…

A:

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

A: When a particle move on a circular path , the direction of velocity of the particle along the…

Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 51…

A:

Q: 86. If f'(x) > 0 for all real numbers x and s(1) đt = 0, which of the following could be a table of…

A:

Q: Solve the following differential equations of 1- yy' = 2y – x; r'y'y'+ xy' = 1 dy x + v

A:

Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

A:

Q: Let f(x) = 9x* + xx² + e2*. Compute f©(x). (Use symbolic notation and fractions where needed.) f9(x)…

A: Compute 5th derivative of f(x)

Q: 14th term of the following geomnetric sequence. Find the 1. 2, 4, 8, 0. 昌 唱

A: Use geometric series concept

Q: al)= gi+ sk vio)= 5), ro) 0

A:

Q: 5² - 13 ニ

A:

Q: f" (x) = cos x, f(0) = 1, f'(0) = 2, f'"(0) = 3.

A:

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

A: To solve the following problem

Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

A:

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Evaluate the line integral / (x +8y)dx + (5x – 4y)dy along the - curve C : x = 8 cos t, y = 16 sin t…

A:

Q: 3. 1- xZ dx

A: The integration of the integral is x4sqrt(1-x2), limit from 0 to 1.

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

A:

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: Find an equation of the hyperbola having foci at (3, -11) and (3, 7) and vertices at (3, -4) and (3,…

A:

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: Find V x (V × F) if F(x, y, z) = 4.xyj+2xyz k. ▼ × (V × F) = %3D

A: ∇×F=i^j^k^∂∂x∂∂y∂∂zPQR  for a vector F=Pi+Qj+Rk in terms of x,y,z

Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: AX = B is a matrixial representation of a lineal system of equations. Over the augmented matrix (…

A: Here we have to choose the correct option.