between the curve of the function f(x) = 2x and the x-axis over the interval [-3, 3].

Q: Find the arclength of the curve x with 2 ≤ t ≤9. 1 3 Y - 2

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Q: b) 21 +2 01-8y=2002 dx

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Q: Use the limit definition of the definite integral to determine the value of the definite integral…

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Q: gradient of the line joining the points (3, 5) and (2, 8) is

A: Given query is to find the gradient of the line.

Q: 6.) so +3 dx 2xe+²+

A:

Q: Determine the measures of angles between diagonals of the rectangle whose vertices are:

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Q: 4. Find the first and second derivatives of the function: f(x)=√x².

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Q: What would projvu be?

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Q: 2) Evaluate surface z dv where E is the region enclosed by the Z = x² + y² and the plane Z = 1

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Q: Simplifying the logarithmic expression log, b³ - 3 log, a + 5log, a¹b will give you m+nlog, a The…

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Q: 8. Find the differential of each function: (a)y=tan(cos.x) : (b) y=- Answer D

A: 8) a) y= tan(cosx)

Q: 13. Find the domain, range, and right end behavior (xx) of each function below: (a) f(x) = -2(1.3)…

A: We know an exponential function is valid for all real number and it gives always positive real…

Q: Find the general solution of the given system. dx dt dy dt (x(t), y(t)) = = 4x + y = -2x + 2y

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Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: -8 -6 -15 4-5 S 4 + Ox O Using the graph of f(x) above, answer the following. If a limit or…

A: Given Graph:-

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

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Q: 21. Expand completely: logn X y² - 9 -

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Q: Find lim_ (x+3)² x→-5

A: Given: limx→-5x+32

Q: Find the equation for the parabola that has its focus at (−35/4,−3) and has directrix x=-29/4.

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Q: Find the indefinite integral. x7-9 DOT dx 4

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Q: Given the function: a. Find f'(x) and f"(x) b. Determine the following properties of the graph of f.…

A: Please see the below picture for detailed solution.

Q: Suppose parametric equations for the line segment between (3, 0) and (4, — 10) have the form: [x(t)…

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Q: The graph of a function g is given. 1 = 0 Consider the integral I when answering the following…

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Q: Evaluate the integral. ['w² w² In(w) dw

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Q: For the D.E. d+7x²y = 0 y(0) = 2, the value of y(1) is

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Q: Which of the following differential equations is solvable by the transformation y=vx, where v is a…

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Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

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Q: Find f'(5), if f(z) = (4z² + 5x) (2x² - 8)

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Q: Find the sum of the following series. If it is divergent, type "Diverges" or "D". n=0 7" 9nn!

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Q: Find the following antiderivative. J dx (x ln x) In (In a

A: To evaluate the antiderivative

Q: Find the x-coordinate of the point on the graph of f, between points P and Q, at which the line…

A: Let (x,y) be the point at which the tangent to f(x) is parallel to line PQ.

Q: he tangent line to s(t) a(t) at the point

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Q: Σ n=1 5 n(n+1) 1 (-2)] (Hint: use partial fractions)

A: To find the convergence and divergence of given series.

Q: Evaluate *(1-x)¹/3 da. Hint: use substitution. Select one: O a. 27 220 O b. 0 с. O d. 28 27 140

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Q: Find the indicated partial derivatives of: θω Ər dw მs dw Ət || || || w = √2r² +68² + 6t².

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Q: lim cos TX x→1

A: Given query is to find indicated limit.

Q: Suppose that the monthly marginal cost for a USFS approved wildfire water pump is C'(x) = 40x + 715…

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Q: Find and classify the critical points of f(x, y) = 3xy - x³ - 2y².

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Q: (b) Parametric equations: Rectangular equation: Parametric equations: y=2 sint X || y= 0 11/13x + 4…

A: Ques (a) Rectangular equation: x2+y2=4x2+2sint2=4x2=4-4sin2tx2=41-sin2tx=41-sin2tx=4(cos2tx=2cos(t)…

Q: - [P] = [In(1+1²)] dt = IP xp J (e) (d)

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Q: Let f(x) = lim x →-5- - - 6 48 x-3 Compute the quantities below. Write "DNE" if the limit does not…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

A: We have to find the critical points and absolute extrema.

Q: Prove that the inverse hyperbolic function can be written in terms of logarithms: cosh¹x =…

A: We have to prove that cosh-1x=lnx+x2-1 for x≥1.

Q: Use sigma notation to write the sum. 1 5(4) Σ i = 1 + 2 5(5) + 3 5(6) + + 10 5(13)

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Q: How do you measure distance along a smooth curve in space from a preselected base point? Give an…

A: To find: measure distance along a smooth curve in space from a preselected base point

Q: Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit. [°…

A: Here is the solution:

Q: 4) Write an equation for a sphere centered at the point (4,6,-1) with radius 8

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Q: Find the area enclosed by the ellipse a cos(t), y = b sin(t) with 0 ≤ t ≤ 2.

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Q: 1 X. Xx4 + 4 +8 dx

A: