Find the number in the interval [0, 2] such that the number minus its square is as follows. (a) as large as possible ___________________ (b) as small as possible

Q: Use the quotient rule to find the derivative of cot z. Simplify its derivative as much as possible.…

A: To solve this question we would use the following supporting formulas   ddxcosx=-sinx ddxsinx=cosx…

Q: Differentiate: e6x² A) 6e6x²-1 D) 12xe*-1 B) e 6x² E) 12xe6x² C) 2ex-1 F) 12xe*

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Q: Which of the following functions is homogeneous of whose degree of homogeneity is 4. A. f(x, y) =…

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Q: Use any method to find the volume of the solid generated by revolving the region bounded by the…

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Q: Find the equation of the tangent line to the graph of f(x) = √x + 100 at the point (0, 10).

A: Given query is to find the equation of the tangent.

Q: 9. y = ln *³(x-¹)(use properties of logarithms) (x+1)4

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Q: Determine the orthogonal trajectories of the one-parameter family of lines y - Cx = 0. A. x2 + y2 =…

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Q: Variables

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Q: Find the slope of the tangent line to the curve f(x) = x³ - 4x at the point where x = 0. A) 0 B) - 4…

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Q: Suppose that f(x, y, z) = x²yz — xyz³ is a function of three variables. 1. Find the gradient of f(x,…

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Q: 1. x²sin (y) dx - cot(y) dy=0

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Q: Use the formula for nCr to evaluate the expression 12C5.

A: Given: the given expression n: 12C5. Formula Used: Crn = n!r!(n-r)!

Q: Find y to the second derivative. y=5excos(x)

A: To find second derivatives..

Q: PLOT THE GRAPH FOR THE GIVEN CURVES AND CONDITIONS BELOW Need to find out the differential equation…

A: We have to plot the graph.

Q: 3 Each limit repr number a. State m -0 √9+h-3 h

A: Given query is to find f and a.

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Find an equation for the plane that passes through the following points. (3, −1, 5), (0, 0, 6), and…

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Q: Phone Charges The monthly cost C, in dollars, for callsfrom the United States to Japan on a certain…

A: Since you have posted a question with multiple sub_parts ,we will solve first three sub parts for…

Q: E. Generate solution of the first-order differential equations using 1. Separation of variables/…

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Q: Graph the functions in Exercises 23-26 in the ts-plane (t-axis horizon- tal, s-axis vertical). What…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: y-values 6 8 7 6 5 4 32 1 If f(x) = f'(1) = g(x) h(x) ' g(x) 2 3 x-values then 4 Out y-values S 4 3…

A: To find the derivative of f(x) at x=1.

Q: Find d2y/dx2 if x = 3 - 2z and y = z2 - 3z3

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Q: Let F(x) = f(x7) and G(x) = (ƒ(x))¹ . You also know that a = 7, ƒ(a) = 2, ƒ'(a) = 15, ƒ'(a¹) Then…

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Q: What is a periodic function? Give examples. What are the periodsof the six basic trigonometric…

A: Function: In mathematics, a function is an expression, rule, or law that establishes the…

Q: a. Graph the function ƒ(x) = sqrt(1 - x2), 0<= x <= 1. What symmetry does the graph have?b.…

A: The given function is: f(x)=1-x2,0≤x≤1. It is required to find the symmetry of graph.

Q: Use the addition formulas to derive the identities in Exercises 31–36. 31. сos = sin x 32. cos x…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 1. Express the given function H(x) as a composition of two functions f and g such that H(x) =…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: lim S/GX X+10 5 G1-x

A: To evaluate the given limit of the function.

Q: The point 2 is in the range of the function given by f(x, y) = True False 2x² x² + y²

A: We can check whether the statement is true or false .

Q: Write a word problem that can be solved by evaluating 7P3.

A: Given: 7P3. Formula Used: Prn = n!(n-r)!

Q: me of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At…

A: Volume of cube is side cube

Q: 1. y = 4x+Czxe *

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Q: What happens if you take B = A in the trigonometric identitycos(A - B) = cos Acos B + sin Asin B?…

A: The given identity: cos(A - B) = cos Acos B + sin Asin B To check what happens if B = A .

Q: Use synthetic division to find the quotient and the remainder when the first polynomial is divided…

A: See the details solution in below

Q: dy For items 13-14, consider the function y=√ 6x-2 whose derivative is given by dx 3₁√/6x-2 2(3x -…

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Q: S x5 ex dx

A: We will use method of integration by parts. We will perform step by step process to finally solve…

Q: = = '1' (a) 21 = 6e-i (b) z2 = 21, (c) 23 (d) z4 = 21 + Z2, (e) 25 = 21 - 22. 2122, 2п 3

A: We have given some complex number problems in Euler's Form. We have find the real and imaginary…

Q: PROBLEM: Find the differential equation of the family of hyperbola with center and transverse axis…

A: Solved below

Q: Consider the ellipsoid x² + y² + 3z² = 8. Find all the points where the tangent plane to this…

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Q: Evaluate: 1. lim [√x² + x − √x² + 4] = X→ +∞ 2. lim [(x²-In(x + 1)) cotx] -0-x

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Q: The highway mileages of 147 cars are in a file named CARS2.+ These cars are 2003 models. Find the…

A: Mean Formula The mean formula is defined as the sum of the observations divided by the total number…

Q: In Exercises 55 and 56, solve for k. 55. a. e = 4 b. 100e10k = 200 c. /1000 = a 56. a. ek = - 4 c.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: The original 24 m edge length x of a cube decreases at the rate of 4 m/min. a. When x = 5 m, at what…

A: Topic- Application of derivatives We are given, Original edge length of cube=24mrate of decrease of…

Q: Effect of Price on Demand for Tires Suppose the quantity demanded weekly of the Super Titan radial…

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Q: a. xy³ dx + (y + 1)e¯*dy = 0

A: xy3dx+y+1e-xdy=0

Q: Find parametric equations representing the line segment joining P(-3, 2) to Q(2, -1) as (x(t),…

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Q: What are the important types of functions frequently encounteredin calculus? Give an example of each…

A: Function: A relation between a collection of inputs and outputs is known as a function. A function…

Q: Graph the polynomial given below by first selecting the number of points you will need, then move…

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Q: Find the partial fraction decomposition of the integrand. 3 'x(x²+5)* dx = O dx

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Q: A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a…

A: Given data, n=40 r=8