Express the equation in logarithmic form. 1 wlr -4 = 81

Q: Find the y-coordinate of the y-intercept of the polynomial function defined below. f(x) = −2x(2x² +…

A: Given; We know that the y-intercept is an (x,y) point with x=0. So, we get that f(0) = 0.

Q: Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4.…

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Q: #solve the following lup x²=-2x-y Misob & chris y'= 6x-78 y (o) = 7 x(0)=3 Then find x(0.25) to at…

A: Given system x'=-2x-yy'=6x-7yand   givn condition x(0)=3  and   y(0)=7

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

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Q: You are a lifeguard and spot a drowning child 40 meters along the shore and 50 meters from the shore…

A: Distance along the shore= 40m Distance from the shore= 50m Run speed = 4 m/sec  Swim speed = 0.9…

Q: Solve trignometric equation a) cosetan e-cost=0 b) cos(2x)-gnx = 0 for 0≤x≤ 1/2

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Q: Find the slopes of the curve 3 4 irve y4=y2-x² at the two points shown here. 1 2 √3 2 Q 57 The slope…

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Q: Let g(x) 10x + 12 3x + 6 Find the derivative of g'(x). g'(x) =

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Q: 9. A store sells about 360 calculators per year. It would cost the store $8 to store one calculator…

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Q: π 5) Find the exact value of sec- 8

A: Consider  secπ8   Formula  secx=1cosx

Q: An equation relating the variables x and y, the values of x and y, and the value of dy value of…

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Q: Sketch the graph of the function below, including correct signs, x-intercepts a intercepts. f(x) =…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 3n 201 3n…

A: Use the comparisonn test

Q: The polynomial of degree 3, P(x), has a root of multiplicity of 2 at x = 1 and a root at x =…

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Q: 1 The graph of y² = x³ is called a semicubal parabola. Determine the constant b so that y=-3x+b…

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Q: Problem 4. number, using the following steps. In(x) xxx0.01 (a) Compute lim (b) Compute lim In(x)…

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Q: QUESTION 5 Given f(x,y) dA, where D is the region bounded by y = 2x² and y = 1 + x². Determine and…

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Q: Consider the differential equation (2x-xy) dx-2dy=0 with the initial condition y = 1 when x = 1.…

A: We need to find approx value.

Q: How many x-intercepts would the function shown below have? f(x) = (x² − 5)

A: given that,   f(x)=x2-5   how many x-intercepts would the function have?

Q: 1 √1-y² 84. :// -√1-y² (2x + 4x³) dx dy

A: To evaluate the following double integral.∫01∫-1-y21-y2 2x+4x3 dx dy

Q: Choose the correct option for the following two statements and provide justification for your…

A: Please see the below picture for detailed solution.

Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

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Q: Show using the MVT the equation x^3-x-2 = 0 has one real solution on the interval [1,2] AND…

A: Using mean value theorem f'c=fb-fab-a Where, a=1,b=2 f'x=3x2-1 f'c=3c2-1 f2=23-2-1=5 f1=13-1-2=-2

Q: Sunday - let lim (1x) = -8 and lim glx) = -5. Find lim [-5(1x) -8960) 2-2 x > ² [ 3+ g(x) X42 Do…

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Q: 10. Find the Taylor polynomial P4 for f(x) = In x at xo = 1. (a)_1+ ²(x-1)=(x-1)² + ²/(x-1) - 1 4 5…

A: Given f(x)=ln x    x0= 1we want to find taylor polynomial P4(x)

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = 2x3 + y4 + 8,    D = {(x,…

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Q: QUESTION 2 In the figure below a = (3,1,0) and b= (2,5,0) X Z B TO If 0 = π, what are both a b and a…

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Q: Evaluate the following improper integral. If the integral is divergent, enter "divergent" as answer.…

A: As we know the Power rule: ∫xndx=xn+1n+1+C   The given integral is: I=∫01x1-x23dx   ...1

Q: Use the given graph of f to find a number 8 such that if 0 < |x - 3| ≤ & then [f(x) − 2| < 0.5. y 8…

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Q: Find all critical points and then use the first-derivative test to determine local maxima and…

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Q: Problem 1. True/False. ex ex lim x 0 x lim x 0 1 Think carefully about the conditions for…

A: Here we have to state whether the statement is true or false.

Q: Find the local quadratic approximation of f(x) = x³ to find the approximation of 1.03³ at xo = 1,…

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Q: Find the indefinite integral. (Use C for the constant of integration.) [x² x cos 7x² dx

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Q: Graph the parabola. y=x²+10x+27 Plot five points on the parabola: the vertex, two points to the left…

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Q: QUESTION 12 Interpret lim 4xy² along x = (x,y)-(0,0) x²+3y4

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Q: The polynomial of degree 3, P(x), has a root of multiplicity of 2 at x = 1 and a root at x =…

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Q: Question 3. Let G be the region within the cylinder x² + y² = 1, above the xy-plane and √√6x² + So +…

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Q: A continuous function y = f(x) is known to be negative at x = 1 and positive at x = 4. Why does the…

A: A function with no breaks is a continuous function.

Q: Find the indefinite integral. (Use C for the constant of integration.) [x² x cos 4πx² dx

A: Given: I=∫xcos4πx2dx   ...1   Use the common integral: ∫cosxdx=sinx+C

Q: 2. A carpenter has a 10 foot long board to mark off a triangular area on the floor in the corner of…

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Q: 5x² R is the region bounded above by the graph of f(x) = 3x - and below by the x-axis over the…

A: Given:       fx=3x-5x22 interval 0,1  Volume of solid formed by revolving around y-axis:…

Q: Find the derivative of ?(?)=32?3+14?2+2?+1f(x)=32x3+14x2+2x+1 where ?=2x=2.

A: given f(x)=32x3+14x2+2x+1

Q: Find the location of the absolute maximum and absolute minimum of the function on the given…

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Q: 6 When a theater owner charges $5 for admission, there is an average attendance of 180 peopre. For…

A: Concept: The slope of a function can be found in its first derivative. The slope of the curve grows…

Q: The following graph shows a rough approximation of historical and projected median home prices for a…

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Q: Find the scalar and vector projections of b onto a. a=(3, 6, 2), b=(3, 1, 1) compab= proj b=|

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Q: A value of sinh x or cosh x is given. Use the definitions and the identity cosh²x - sinh²x = 1 to…

A: Given that sinhx=-125Our aim is to find the value of cschx=?

Q: Find the limit 2 ·lim t²-16 t-4 t³-64 3

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Q: QUESTION 15 Interpret the divergence of F(X,Y,Z) = (x2y.yz², zx²) at a point (1.-5,1).

A: The given vector is:F(x,y,z)→=x2y, yz2, zx2

Q: Evaluate the definite integral. Use a graphing utility to verify your result. fixe- -3x² dx

A: integration