d) f(a) = (2a-1)² 2a + 5a

Q: Je²² e² sin (e)dr

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the integral by interpreting it in terms of areas. 4 to −9(1 − x) dx

A:

Q: The regions A, B, C, and D in the figure below are bounded by the graph of the function f and the…

A:

Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

A:

Q: Find the tangent plane to the equation z = - 3x² + 2y² + 4y at the point (4, 1, - 42). 2 = Check…

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

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given figure  with areas Now V=∫010f(x)dxV=∫03f(x)dx+∫35f(x)dx+∫57f(x)dx+∫710f(x)dx

Q: Let f(x) = 4x + 7 – 17e². Then the equation of the tangent line to the graph of f (0, -10) is given…

A:

Q: Find the center and radius of the sphere with equation (z + 3)² + (y + 1)² + (z+4)² = 1 Center:…

A:

Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

A:

Q: Given x = y² +y + 1 from 0≤y=2 The Arc Length of the given curve over the interval is a. 7.38 units…

A: I have stated the used formula in the solution

Q: Determine whether the following vector field is conservative on R³. If so, determine the potential…

A:

Q: Let f(x) = 2log₁(x) f'(x)= ƒ' (6) =

A: We have to solve above question

Q: Let a = -17-23 + 3k and 6 = 67-53-4k. Find a b Check Answer

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: The regions A, B, C, and D in the figure below are bounded by the graph of the function f and the…

A:

Q: TU 8. fz sin¹x cos5 x dx 2 0

A: To find the value of the given definite integral:∫0π2sin4x cos5x dxWalli's Formula:∫0π2 cosnx dx=…

Q: = Using calculus, find the absolute maximum and absolute minimum of the function f (x) [-3,2].…

A:

Q: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

Q: Evaluate the definite integral (3625 - 24) dz using Part 1 of the Fundamental Theorem of Calculus.…

A:

Q: Sketch a graph of a continuous function f with the following properties: (i) f(x)=0 for x = 0 (ii)…

A:

Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

A:

Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

A:

Q: Find a plane through the points (-3,-8,7), (7,-2,6), (-2,8,-4)

A: answer is in next step.  as per guideline i can answer only one question .

Q: Calculate the directional derivative direction Q(5,4) 4 3√-3x²-5xy3 of at P (1,-2) in the

A:

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy (x,y) for the function f. f(x,y) = 5x e 8xy fxx (x,y) =…

A:

Q: Find the equation of the tangent to the curve y = sin(3x) COS(z) at z = 4.

A:

Q: 5₂00⁰ dx 2 3 1.

A:

Q: Find the flux of F across S, [/F. Nds where N is the upward unit normal vector to S. F(x, y, z) =…

A:

Q: Consider the function f(t) = 5 sec²(t) — 9t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A:

Q: What is correct form of the particular solution associated with the differential equationy'''=8?

A:

Q: Rewrite sin(x+ H Enclose arguments of functions in parentheses. For example, sin (2x). sir 20 in…

A:

Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

A:

Q: lim x3 3 3 1 – x

A: Concept: Limit: The value that a function tends to approach as the input value, also known as the…

Q: Answer the following True or False. 1 COS T dz = ln(cos z) +C

A: Our Aim is to answer whether the value of integral obtained is true or false.Given integral…

Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

A:

Q: A tank half-filled with water is in the form of a rectangular parallel piped 5ft deep, 15 ft wide…

A: Answer is c

Q: A body of mass 4 kg is projected vertically upward with an initial velocity 34 meters per second.…

A: Solution is given below:

Q: √x+9 at x = 0. Write your answer in the form a+bx+cnx" n=2 where a, b, and each cn are constants.…

A:

Q: Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

A: This question is related to differentiation, We will solve it using given information.

Q: Let f(x) = f'(x) = f'(9) = 4log7 (x)

A:

Q: 2 (2y² + 5xy 4 Ο α. χ' (y² + 2xy = y + 2) = C O b. x4 (y² O 2y + 4) dx + x (2x + 2y − 1) dy = 0 - -…

A: The given differential equation is; 2(2y2+5xy-2y+4)dx+x(2x+2y-1)dy=0.

Q: face da +C

A:

Q: Evaluate the triple integral g(x, y, z) dV over solid B. B = {(x, y, z) | x² + y² ≤ 10², x ≥ 0, y ≥…

A:

Q: lim x(√16x² + 2 - 4x) X118

A:

Q: Find 13 sin(82)da [13 sin(8x)dz = +C

A:

Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

A:

Q: For each of the following, use the table of integrals found in the textbook to find the an…

A: Answer is in next step. please give a like !!

Q: Evaluate: (In x)² x -dx - +C

A: Topic - indefinite integral ∫xndx=xn+1n+1+C

Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=<-5t5-3,4e-4t,-5sin(2t)>

Q: 4. Consider the vector a=(-2,3,-1). [ [K/U] Find the magnitude of the vector ä. b) Find an unit…

A:

Q: For the function f(x) = two periods. Amplitude: A Period: P = -2 sin HARE Number Xx 37 4 Enter the…

A: