Problem 6. Find a function f(x) whose derivative is f'(x) = x² √√√x³−1+x³ and which satisfies f(2)= 1. State the Integration by Parts formula.

Q: Consider the partial derivatives Is there a function f which has these partial derivatives? Yes Ⓒ If…

A: We need to write down that is there any function having the given partial derivatives.

Q: D; E; Factor the expression. 3x²+11x-20 Rationalize the expression and simplify. √14 √5-2

A:

Q: 2. (6x+y²) dx + (2xy-3y²) dy =o

A:

Q: Siven f(1, y) = x² – 7y, find lim f(1 + h, y) – f(1, y) h→0 h

A: Topic:- limits and continuity

Q: Find the limit as →∞ and →∞. Use this information, together with intercepts, to give a rough of the…

A: The given equation is y=x3(x+2)2(x-1) We have to find the x-intercept and y-intercept

Q: What rational function satisfies these conditions? lim f(x)=10 (x-->3), lim f(x) =2 (x--->…

A:

Q: Find f'(x)) D f(x) (2) f(x) 3x³ +5x²12-2 2 6x -3x + 2x12 2

A:

Q: #1 Cπ/2 ST 0 (8 + 4 cos x) dx

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

Q: Compute the given integral. 1 x² + 36 Add Work -dx = Submit Question +C

A:

Q: f(x) is graphed below. Find each value. 10+ 9 8 7 6+ 5 4 3 2 10-9-8-7 -6 -5 -4 -3 -2 -1 lim 2-6 lim…

A:

Q: For the given function f(x) and numbers L, c, and > 0, find an open interval about c on which the…

A:

Q: Consider the differential equation dy/dx = 5-y. (a) Either by inspection or by the concept that y =…

A:

Q: Use linear approximation to approximate ✓49.1 as follows. Let f(x)=√x. The equation of the tangent…

A: Tangent line equation of fx=x at x=49

Q: A closed box is in the shape of a rectangular solid with dimensions x, y, and z. Suppose each…

A:

Q: Find all values of x, 0 < x < 2π, for which the graph of f has a horizontal tangent (= all points at…

A:

Q: Solve the following for C. (Assume that C > 0) C (4x+8) dx 0 C = = 90

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

Q: b. 14-x²|dx

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

Q: -4 -2

A: We have to find the following conditions according to the given information

Q: Determine the dot product of (0, 5, 10) and (-3, 1, 0).

A:

Q: 16. (x − y ln y + y ln x) dx + x(ln y − ln x) dy = 0.

A: The given differential equation is; (x-ylny+ylnx)dx+x(lny-lnx)dy=0

Q: Determine whether the function is even, odd, or neither f(x)=tan(x) cos(x)

A:

Q: The graph below is the function f(x) -5 -4 -3 -2 -1 -1 -2 -3 Find lim 2-2 Find lim z-2¹ 4 3 2 1 f(x)…

A:

Q: Calculate the first, second, and third derivatives of y(x) = x-19/5 (Use symbolic notation and…

A:

Q: 8. After p practice sessions, a student could perform a task in T (p) = 36(p + 1) 3 minutes. Find…

A: After p practice sessions, a student could perform a task in T(p) = 36(p+1)3 minutes We have to find…

Q: Use the second derivative test to identify any critical points and determine whether each critical…

A:

Q: Once a certain tree reaches 3 feet, its height is measured at the end of each of the next several…

A: The appropriate relationship has multiple of 1.6

Q: Given the demand equation x = 9+ 21 p' Elasticity of Demand = Therefore, demand is where p…

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: given that,y=x5(1+2x)7 we know that, derivative formulas: (uv)'=uv'+vu' ddx(xn)=nxn-1

Q: Calculate the cross product assuming u xw = (8,6, -2) (Use symbolic notation or fractions where…

A:

Q: П Find the length of the curve y = In (2 sec x) from 0≤x≤6 Set up the integral that gives the length…

A:

Q: If f(x) ƒ'(x) = f'(5) = = tan x sec x 2

A: Topic- Derivative of a function  Note: As per bartleby guidelines, we are supposed to answer only…

Q: D Question 5 Find dy/dx, given the following: y = | L y P (x²+2x)² 3 (3x²+2) (2³+2x)² + = V (2x-4) 2…

A:

Q: Find the derivative of y with respect to t. y=cos¯¹ (√2t) dt (Simplify your answer. Type an exact…

A:

Q: B. 3y² + 2xy = 8 dy dx m TL Equation of tangent line m. NL Equation of normal line

A: Given equation of curve:- 3y2+2xy=8

Q: 5. For the constant numbers a and b, use the substitution = a cos² u + b sin² u, for 0 <u<, to show…

A:

Q: 3. f(t) = 3t - t², (0,0) 4. f(x) = 3-5x, (-1,8) 5. g(x)=x²-9, (2,-5)

A:

Q: direction: find the indefinite integeal   x-3  / x^2 + 1

A: Given query is to find the integral.

Q: Solve the Bernoulli Equation and Explain Each Step 2 B.y + y = xy², y(0) = ¹/

A:

Q: y=f(x) Fig. 2 a) lim f(x) X-4- d) lim f(x) x-3- b) lim f(x) X-4+ e) lim f(x) c) lim f(x) x→4 f) lim…

A:

Q: The cost function of producing x items is C(x) = 4x² - 12x + 500. a) Find the marginal cost function…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Graph the curve. 4e cos(t), y 4e'sin(t), 0 stsn

A:

Q: Evaluate the given integral. Use exact values. 52+17 (x+3)(x + 4) √ dx = Question Help: Video Add…

A: Topic:- application of integration

Q: II. Determine the point(s) of intersection, m, and m₂, and the angle(s) of intersection of the given…

A: Given:     The curves 2y=2x2-6x+7                       y=x2-3x+72 ...1    Curve 2y=x+4…

Q: Use the method of Lagrange multipliers to find the maximum and minimum values of the function…

A:

Q: Find the area of the region bounded by the graphs of the given equations. 2 y = 3x+18, y=x

A: Here is the solution:

Q: Calculate the scalar triple product u (v x w), where u = (1,5, 0), v = (-8, -9,9), and w= = (4,…

A:

Q: Maximize f(x, y) = √11-x² - y², x + y - 2 = 0.

A: The given function to maximize is: f(x,y)=11-x2-y2 with the constraint g(x,y)=x+y-2=0...(1)

Q: 2. Find the Inverse Laplace Transform of the following: b. L-¹{2+15+13)

A:

Q: 11. f(x) = a sinx - b cos x + c

A: f(x) = asinx -bcosx +c  Given We have to differentiate it . Steps are given below

Q: I. Use Lagrange multipliers to find the minimum and maximum values of f(x, y) = x + the restriction…

A: