Consider the function Evaluate the definite integral. f(x) = fx if x < 1 {if x ≥ 1 [1 f(x) dx

Q: Find the arc length of f(x)=ln|x| over [1,3]. Round answer to two decimal places

A: We will find the required arc length.

Q: 14x - 42 x² + x - 12 1. Write the function in completely factored form: Consider the function f(x) =…

A: Concept: The line x=L is a vertical asymptote of the function y=14x-42x2+x-12, if the limit of the…

Q: y" + y = 2, y(0) = 4, y' (0) = 3 (A) y = 2 sint + 3 cos

A: given y'' + y = 2 D2y + y = 2(D2 + 1 ) = 2 for complementary solution D2 + 1 =0D = ±iD = 0…

Q: Find an nth degree polynomial function with real coefficients satisifying the given conditions n=4…

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Q: Compute the directional derivative of fat the given point in the direction of the indicated vector.…

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Q: A rectangular metal tank with an open top is to hold 4 cubic feet of liquid. What are the dimensions…

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Q: Question Determine the absolute error when using the rhidpoint rule to find ³ (8x² + 5) dx using 3…

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Q: Consider the function f(x) = = Based on parts b through e, f(x) has a maximum of y = when x = when x…

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Q: SOLVE a, b, c, d, e, f, g, h, i, and j SOLVE THE FOLLOWING IN MS EXCEL USING GAUSS ELIMINATION DO…

A: Gaussian Elimination is one of the methods to solve a system of linear equations. In This Method we…

Q: (ex + ln y + ²) dx + ( + Inx + siny) dy = 0 y(2x² - xy + 1)dx + (x - y)dy = 0

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Q: Find an equation of the tangent plane to the surface at the given point. y (1, 9, 9) f(x, y) = −9x +…

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Q: 1 L'e ex dx. Let consider a) Apply the composite midpoint rule with m = 4. Compute error by…

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Q: Find the general solution in the form y = yc + yp. y'' + 4y' + 5y = e-2tcost

A: y'' + 4y' + 5y = e-2tcost Find genral solution

Q: Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of…

A: Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of…

Q: ASK YOUR TEACH The sum of the perimeters of an equilateral triangle and a square is 17. Find the…

A: Given data÷ Sum of perimeter of equilateral triangle and square is 17. We need to find the…

Q: A plane takes off at an angle 6° from the horizontal. Given that the plane is traveling at 530 mph…

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

Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

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Q: Determine if the series below converges or diverges by comparing it to a p-series using the…

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Q: point The graph of the function f(x) = 3-5 can be obtained from the graph of g(x) = 3 by one of the…

A: Domain:- The set of all those input variable such that the function at those values exists.Range:-…

Q: If 1 f(x) = coth-¹√√x² +5 then f'(x) = 0

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Q: Use substitute method to solve the two system ec -= x - 4y (1) dx #1: dt dy -= x+y (2) dt

A: As per our guideline we supposed to answer only first question  Given system dxdt=x-4y…

Q: Find the indefinite integral. (Use C for the constant of integration.) (-8x7) dx |

A: Let A=∫e^-X^8(-8X^7)dX        →  ∫X^n=X^(n+1)n+1

Q: Given the scatter plot shown, determine if the correlation is positive, negative, or if there is no…

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Q: Find the slope of the tangent line to the curve y x²+4x+7 7x+2 at the point (1,3).

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Q: 7. Start from the given graph of y = log5 (x), then sketch the graph of the following function. f(x)…

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Q: Question Evaluate the integral. So 70 Give an exact answer. If the integral is divergent, enter Ø.…

A: We will find the required integral.

Q: Find the exact value of the given expression. tan(cos-¹(²)) 2 3 4

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Q: 17. The science club members are to work in pairs on an experiment. a) If there are eight members…

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Q: 3. The limits below do not exist. Verify this by showing two different pathways that result in…

A: limx, y→0, 0xy2x2+y4along path x=0=lim0, y→0, 00· y202+y4=lim0, y→0, 00=0along path x=y2=limy2,…

Q: Find the third derivative of the given function. g(t) = √9t + 3 _g"(t) = X

A: We need to find out the triple derivative for the function given.

Q: Let P be the plane that intersects the x-axis at the point (1, 0, 0), the y-axis at the point (0, 2,…

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Q: f(x) = x² - 11x + 30 g(x) = x - 5 (f+g)(x) = (f- g)(x)

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Q: Solve the given differential equation (where the function is subject to the given conditions) by…

A: Topic = Differential Equation

Q: Unit Find the vector = (-3,₁27, in the direction opposite to V

A: Topic = Vector

Q: Given that f(x) (a) (f + g)(3)= (b) (f - g)(3)= (c) (fg)(3)= (d) (-) (3)-[ = x² - 7x and g(x) = x +…

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Q: ASK YOUR TEACHER A rectangular package to be sent by a postal service can have a maximum combined…

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Q: 191-21-A 20 VV 10 -2 -4

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Q: Describe the triangular region whose vertices are at (0, 0), (1, 0), (1, 2) as set in the polar…

A: Answer is in step 2.

Q: Consider the function f(x)=2x−6/x. Find the exact value of all numbers that satisfy the conclusion…

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Q: Which of the following statements imply that thas a vertical asymptote at ? Make sure to select the…

A: We have given the function g(x) and the vertical asymptote at x=3.

Q: Find direction Vector a that has the same as (-6,5,67 but has length 4

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Q: 3. Sketch the vector-valued function r(t) = (sin(2πt), t, 3 cos(2πt)), indicating direction.

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Q: The boxplot below shows salaries for Actuaries and CPAs. CPA HC Actuary 30 40 70 80 90 100 110 Q 50…

A: First we will plot the minimum, first quartile, median, third quartile, and maximum as shown below

Q: Consider the function f(x)=4x2 −48x+3 on the interval [2,10]. Evaluate this function at the…

A: Topic = Functions

Q: 0 Exercise 7 Limits The following graph of the function f satisfies limf(x) = 2 . For & = 3 find a…

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Q: Use any method to evaluate the integral. S 243 dw w²√√81-w² 243 dw w²√√81-w² W (Type an exact…

A: Given data:- ∫243w281-w2 dw

Q: Evaluate the integral order of integration. NOTE: Enter the exact answer. 4 [.² 5² * ے والی ام dx…

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Q: Sketch the situation if necessary and use related rates to solve. A 6 ft tall person walks away from…

A: We have to find part 1, 2 and 3.

Q: Find the rate of change of a population of size P(t) = ³ + 4r + 10 at time! = 4. The rate of change…

A: P(t)=t^3+4t+10         rate of change=dP(t)dt             dt^ndt=nt^n-1

Q: -6t Find the equation of the tangent line to y = e at t = 0. Y

A: Given Data : We have given a function y=e-6t .   Required : We have to find equation of tangent line…