Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4 trapezoids. (A) з (В) 2.6 1.973 (D) 2.760

Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

A:

Q: Find the accumulated amount if AED 6,000 is deposited at 2.5% compounded semi-annually for 5 years.…

A: Given query is to find the amount accumulated.

Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

A:

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

A:

Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

A:

Q: e

A:

Q: 1. dt 15. y= 17. y 0 tan 0 d0

A:

Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

Q: Find the interval of convergence for the Maclaurin series expansion for f(x) = e".

A:

Q: xe*y dy dx

A:

Q: Recall the geometric series 1/(1 − x) = 1 + x + x^2 + x^3 + x^4 + . . . for |x| < 1. Determine the…

A:

Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x8 1 g(x) 5x + 1 (Express numbers in…

A:

Q: Apply the Ratio Test to each series to determine whether the series converges, or state that the…

A:

Q: Find curl (2z i + 3x j + 6y k). curl(2z 2z i + 3x j+ 6y k) = ( i )i + ( i j + ( i )k

A:

Q: 25. dx is 1 (B) (©) ! (A) 2e (D) (E) divergent

A: see below the answer and calculation

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

A:

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

A:

Q: dx 1-e-* Evaluate A. 2ln|e* – 1|+ c B. Inle* – 1|+x +c C. 2 In|e* – 1| +x+c D. Inle* – 1|+ c

A:

Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

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

A: Given points,  P(0,0,0), Q(4,2,4)

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 3 r(t) = e"i+ etj 9ts K(t) ||

A:

Q: Find r'(t). r(t) = 6 cos (t)i + 3 sin3(t)j + k r'(t) =

A: Let's find.

Q: Find curl(3z i+ 4x j+ 8y k). curl(3z i+ 4x j + 8y k) = ( )i + ( i )j+ ( )k

A: We need to find curl of given vector.

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: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

A:

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

A:

Q: Consider the following algebraic functions. y = 1/x2 y = 0 x = 2 X = 7 Sketch the region bounded by…

A: Given :   y=1/x2 y=0 x=2 x=7

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A:

Q: NC2)=

A:

Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

A:

Q: O An ellipse in the plane x axis, minor axis of length 14 parallel to the y-axis. = 1, center at (1,…

A:

Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables æ, y, z)…

A: Given problem:-

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: Represent the plane curve by a vector-valued function

A:

Q: Find the area of the region enclosed by the curves y = x² and y integrating with respect to y. = 6x…

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) : = 6ti –…

A: Solution is done in step 2

Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A:

Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: Find V· (V x F), if F(x, y, z) = 7e"*i+ 9xe"j – 8e"²k. V· (V × F) =

A:

Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

A:

Q: Use the Babylonian's formula to calculate the circumference of a circle with diameter of 30 units.

A:

Q: Show

A:

Q: 3. The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be…

A:

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A:

Q: Find div F and curl F if F(x, y, z) = 13y"z'i – 10x°z*j – 7xy°k. div F= curl F=

A:

Q: dy Solve the derivative dx for the function: x = e'sint ; y = etcost

A: