6.1.5 Exercises 1. Area between two power functions. Find the area of the region between y = x¹/² and y = x¹/5 for 0 ≤ x ≤ 1. area = Activate

Q: Evaluate the following limits, making sure to justify your calculations as much as possible: lim…

A: See this solution in below.

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

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Q: For what value of p does the sum of roots of the equation 6x² - 3px + 5 = 0 equal the product of…

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Q: DIRECTIONS. Indicate the degree and determine the solution of the following equations. Homogeneous…

A: Let's solve differential equations by using homogeneous Function.

Q: 32. Sketch the following vectors, and find their components and lengths: (a) 4i +3j - 2k (b) i+j+k…

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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: Find an equation for the plane that passes through the point (1, 8, −9)

A: we will find the required equation of plane .

Q: Find the limit. (If an answer does not exist, enter DNE.) lim arctan(eX) x → ∞0

A: We have, limx→∞ arctanex

Q: An object is launched directly in the air at a speed of 48 feet per second from a platform located 4…

A: The position of the object can be modeled using the function ft=-16t2+48t+4, where t is the time in…

Q: 2. Find the 2nd derivative of sin (x²-1) y *2cos(x^2-1) 4x^2 tan(x^2-1) 2cos(x^2-1) + 4x^2…

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Q: PZ π/2 4 2 1 79 -3 -4 The graph of the function f(x) = tan x is given above for the interval a € [0,…

A: Given query is to find indicated limits and vertical asymptotes.

Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Condition for existence of limit at x=a⇒limx→a-fx=⇒limx→a+fx=⇒limx→afx

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: Calculate ㅠ 2 6³ cos² (4x) sin² (4x) dx

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Q: Number

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Q: If ƒ(1) = 5, must lim x approaches 1 ƒ(x) exist? If it does, then must lim x approaches 1 ƒ(x) = 5?…

A: Given :-f(1)=5Now, we have to find that limx→1f(x) exists or not.And if  limx→1f(x) exists then…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6√3 and whose components have…

A: Let vecter to be xi+yj+zk Then length of vector = √(x^2+y^2+z^2)=6√3

Q: Find a formula for each function graphed in Exercises 29. а. b. (1, 1) 2 30. а. b. 2 0 30 (2, 1) 2…

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

Q: Problem 2 There are two points on the graph of the equation y = 2x² +9x² - 60x+12 where the tangent…

A: Explained below

Q: Evaluate f(x) ƒ(1) = f(x + 7) = f(x) + f(7) f(x + h) = = = x + 2 at the indicated values.

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Q: a. Graph the functions ƒ(x) = x/2 and g(x) = 1 + (4/x)together to identify the values of x for…

A: Given:-f(x)=x2g(x)=1+4x

Q: Use the formula for nPr to evaluate the expression 8P0.

A: Given: The given expression is:  8P0 Formula Used: Prn = n!(n-r)!

Q: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart.

A: Given: Total number of cards = 52 Formula used: Probability = Number of favourableNumber of outcome

Q: 6 5 4 3 نا 2 1 ¦ y = f(x) 01 2 3 Enter each answer as a whole number or a fraction, or DNE for Does…

A: The graph of the function is To evaluate: The values of limx→3+fx-4fx+4, limx→3-ffx+4 and…

Q: Consider the following limit statement: lim (9x-3) 15 x → 2 Find the corresponding value of 6 when &…

A: givenlimx→39x-3=15

Q: lim asin x→0 | cr x

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Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

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Q: X 6. What is the instantaneous rate of change at x = 2 of the function f given by f(x) = :-?? X-1

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Q: Let f(x) = √√4x² 4x² + 3x + 5

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Q: Area of a Rectangle A rectangle has one vertex in quadrant Ion the graph of y = 10 - x2 , another at…

A: A vertex of rectangle lies on the following: y=10-x2 Since the area of rectangle is maximized when…

Q: 3 x² + y² the direction of (-3, −3). Then, Suppose f(x, y) (a) ▼ f(x, y) (b) ▼ ƒ(1,4) = = = (c) fu…

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Q: Evaluate (2x + 4)(3x + 2) d dx A) 6 C) 12x + 16 B) 6x² + 16x + 8 D) 30x² + 43x + 8

A: Given query is to find the Indicated derivative.

Q: Sketch a graph of the function f(x) = 2 sin (7x) 2 - 2.

A: The function is given by fx = 2sinπ2x-2 To determine: The sketch of the graph of the function.

Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Given: To find: limx→2- fx , limx→2+ fx, limx→2 fx

Q: ow the steps below for the given function. (Do not use mixed numbers in your answers.) 8x + 5y: we…

A: Given query is to find the derivative by indicated methods.

Q: Filling a Conical Tank Water is poured into a containerin the shape of a right circular cone with…

A: Volume of the cone=13πr2hGiven:-Radius of the base of cone=4 feetheight of the cone=16 feet.and…

Q: DIRECTIONS. Indicate the degree and determine the solution of the following equations. Homogeneous…

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Q: If f(x) = sin x, find ƒ'(x) 5 5 sin(x) cos(x) Find f'(2)

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Q: Indicate the degree and determine the solution of the following equations. Homogeneous DE 1. 2(2x²…

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Q: Find an equation of the tangent line to the graph of the function f defined by the following…

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Q: A sales team estimates that the number of new phones it will sell is a function of the price that it…

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Q: Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the…

A: Concept used: Graphing A graph of a function is a line that represents the function on a coordinate…

Q: If f(x) = 4x² – 5x – 2, find f(x + h) – f(x) ,h + 0 h and simplify.

A: Given expression:- f(x)=4x2-5x-2

Q: A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the…

A: Let the length of fence be L feetLet the width of fence be W feet

Q: Use the formula for nPr to solve:A corporation has ten members on its board of directors.In how many…

A: Given: n = 10 r = 4 Formula Used: Prn = n!(n-r)!

Q: Find an equation for the plane containing the two (parallel) lines v1 = (0, 1, −3) + t(8, 2, −1) and…

A: Find an equation for the plane containing the two (parallel) lines  v1 = (0, 1, −3) + t(8, 2, −1)…

Q: 1. (Section 15.8) The function f(x, y) = z²y has an absolute maximum and absolute minimum subject to…

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Q: Evaluate the definite integral leaving the answer in an EXACT form (no decimals): 5₁²¹0 dx

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Q: Consider the surface xyz = 16. A. Find the unit normal vector to the surface at the point (2, 2, 4)…

A: Given,              xyz=16⇒xyz-16=0

Q: Derive a formula for tan (A - B).

A: To derive:- tanA-B