The graph shown below is f(x) = 2 cos x. If g(x) = Sřf(t)dt , find g '( 1 ). %3D 4 3- 2- 54 3 2 -1 1 2 3 4/5 -2 -3 4- 5- +++++-

Q: Find the gradient of the function at the given point. f(r, y) = 3x+52 +1, (2, 1) %3D O 3i+10 O 3i+5j…

A:

Q: 2. -7-8X-x²

A: Use substitution method to solve this integration.

Q: Determine whether u and v are orthogonal, parallel, or neither. u = -9i + 80j - k v = 9i + j - k O…

A:

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A:

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: 1. write the slope-intercept forms of the equations of the lines through the given point (a) paralel…

A:

Q: Which of the following expressions represents the height of a right circular cone having a slant…

A:

Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A:

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. a = 4 b = 2…

A:

Q: Consider the following. u = 5i - j - k, v = -i + 5j + 2k (a) Find the projection of u onto v. (b)…

A: The expression for the vector projection of u onto v is: projvu=u·vv2v And The expression for the…

Q: your simpest form. factore. S dy (ay+ 13) Jyt4

A: the integration of the integral is 5/[(2y+12)(sqrt(y+4))].

Q: Consider the figures below. (1) (2) 5- 4. Use the rectangles in each graph to approximate the area…

A: Solution is here

Q: For the function glven below, use algebra to evaluate the limits lim f( メー→+ lim f(x), and limf(x)…

A:

Q: s the volume of the frustum of a cone whose upper base is 16 cm in er, lower base 10 cmin diameter,…

A:

Q: Find an equation of the plane with the given characteristics. The plane contains the y-axis and…

A: Plane in 3D: The equation of a plane in 3D is ax+by+cz=d If by is removed, the graph of the…

Q: Evaluate the integral where D is the region bounded by y = x, y = 2, and r = 0. Hint: One order is…

A: We will solve this question by changing the order of Integration.

Q: Sx² et* dx 1 e x (8x2 - 4x + 1) + C 16 (8x2 + 4x- 1) + C e4x 16 e4x 32 (8x2-4x + 1) + C e* (8x2 + 4x…

A:

Q: e length and breadth of the floor of a room are 30 ft. and 20 ft. pectively. Square tiles of 2 ft.…

A:

Q: Which of the following limits is equal to x* dx? (A) lim k 1 3+ n00 k=1 n k* 2 (B) lim E 3+ n n n00…

A:

Q: Direction: Solve the following equations using separation of variables. 4. sin(x)dx + ydy = 0, y(0)…

A: Given

Q: Prove: le* a. ſ csch x = In - |+c lex+1

A: As per Bartleby guidelines rule I am answering only first question as Both question is not subpart…

Q: d) 2x³y + e2y = 4x + 5x²< e) y = (2x* + 4)4*

A:

Q: TOPIC: Applications of Integration Plane Area Area between curves Volumes of Solids of…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: A detailed solution is given below

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

A:

Q: Solve for the following application of first order differential equations. Show your solutions. 5. A…

A:

Q: dy Find for the following expressions: dx a) y = x5 In(3x) b) y = 2 cos (+ 2x³ c) 3x2 + 7x + cos (x)…

A:

Q: (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular coordinates.…

A:

Q: What are the relative extrema of the function f(x)=x3+3x3-24x+7

A:

Q: The Maclaurin series for f(x) = x²e=* is E-o(-1)" xn+2 п! False True

A: I am attaching image so that you understand each and every step.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

A:

Q: Derivatives of trigonometric functions Find the derivative. 1. y = 3sin x +3 cos x - tan x

A:

Q: If a cylinder, a hemisphere and a cone stand on equal bases and have the same heights, what will be…

A:

Q: Integral Calculus: Integration by Parts (Original method

A:

Q: 7. (D+ 3)'y = 15x'e-3* 8. (D- 4)'y 15x²e**. 9. D (D – 2)²y = 16e2 10. D2(D + 3)²y = 9e-3x 11. (D² –…

A:

Q: II Three graphs labeled I, II, and III are shown above. They are the graphs of f,f', and f".Which…

A: Observe the each curve using slope and increasing decreasing properties.

Q: Consider the function f(x) = x/3(x + 2)2/3 whose domain is (-∞, o). (a) Find the intervals on which…

A:

Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: In Exercises 5–8, choose rectangular or polar coordinates to set up an iterated integral of an…

A: To set up the integral of an arbitrary function f(x,y) over the given region.

Q: A hollow cylindrical metallic pipe is open at both ends and its external diameter is 12 cm. If the…

A:

Q: Determine whether P = and Q = are orthogonal vectors. If W = and V =, compute V x W. If W = and V =,…

A: Explanation of the answer is as follows

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A:

Q: Two ships leave a dock at the same time, one sails northeast at the rate of 9 miles per hour and the…

A: Let A and B denote the first and second ship

Q: 2. Consider the graph shown on the right. a) What is the minimum and the maximum value? b) What is…

A:

Q: Where is the function decreasing? * (-1,3) (-2,1) (0,1) O (*-1) O (*, *) O (-1, ) O (-*, 3)

A: A function is said to be decreasing in an interval in which on increasing the value of x, the value…

Q: Solve the system by graphing each equation and finding the point of intersection. -12 + 6 x + 2 y -…

A:

Q: x'sec'ydy – (1 – 2x²tany)dx = 0

A:

Q: In xdx

A: Formula:Integration by parts:∫ uv dx =u∫v dx -∫ dudx∫vdxdxI=∫ x5 ln x dxu=ln x, dudx=1xv=x5I=ln x ∫…