Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a where 0<α<π/2.

Q: An infinite series [x_n converges if the sequence (S_n) of partial sums given oy S_n=x_1+x_2+...+x_n…

A: The given series is 1/[n(n+1)], n from 1 to infinity.

Q: etermine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that…

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Q: 4. If x= sin² and y = 1 when x = 0, then find the value of x when y = 3. 0 O 8 None of these

A: Topic- differential equation

Q: dN dt The rate of change of N is proportional to N. (Use k for the propor kN N(t) = Cekt Evaluate…

A: We are asked to find the value of N when t = 3

Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

A: Given,           fx=cos8x , 0≤x≤π8, a=1

Q: S 2 x ²4x³-5 X e cote 4x³-5 dx

A: The objective of the question is evaluate the indefinite integral.

Q: If f(x, y, z) = 1, then fff f(x, y, z)dV gives the volume of V.

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Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: We have to find the interval on which the vector-valued function  rt = 13t+1i + 1tj  is continuous.

Q: In your own words, explain the central limit theorem. Describe an experiment that could be used to…

A: Explanation:                The central limit theorem (CLT) is a statistical theory that states…

Q: Give the Particular Solution of the following Differenti d²y dy dx2 +2. dx IBC: y(0) = 2 y'(0) = -2…

A: Topic:- differential equations

Q: The sequence whose nth term is given by x_n=sin(n*pi/6) is unbounded is monotonic converges to a…

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Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.) 0,…

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Q: 7. Matrix A is said to be involutory if A² = I. Prove that a square matrix A is both orthogonal and…

A: In this question we have to prove that a square matrix A is both orthogonal and involuntary.

Q: 2.) √ √9-4x² dx x² Solution: Case I let u = asino 2x = 3 sine x = 3 sino 2 dx = ² coso do 2 so, by…

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Q: The marginal average cost of producing x digital sports watches is given by the function C'(x),…

A: Topic- Functions

Q: Let F(x) = f(t) dt and G(x) = g(t) dt, where the graphs of f(x) and g(x) on [−2, 4] are below. -1…

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Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A: Use integration  with respect to x

Q: Find the general solution of the differential equation. (Enter your solution as an equation.) dy 8x…

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Q: Which statement(s) is(are) true? (1) f(x)= |a| is differentiable at 0. is differentiable at 0. ()…

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Q: Question A particle moves along a line with a velocity v(t) = t2-9, measured in meters per second.…

A: Here, the velocity of the particle is: v(t)=t2-9 Now, v(t)=0⇒t2-9=0⇒t2=9⇒t=-3,3

Q: Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric…

A: NOTE: Refresh your page if you can't see any equations. . the exponential decay function is given by…

Q: Use the given information to sketch the graph of f. Domain: All real x, except x = -3; lim f(x) =…

A: From the given information: for x∈-∞,3∪(3, 5) , f'(x)&gt;0 limx→-3-f(x)=∞ and limx→-3+f(x)=-∞ The…

Q: c) Write the polar equation for a conic section with eccentricity 3, a focus at the pole, and a…

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Q: 13. DETAILS ZILLDIFFEQMODAP11 7.R.016. Fill in the blank. (Enter your answer in terms of t.) ^{2²2²}…

A: inverse laplace

Q: 4. Use the special properties of logarithms to solve the following equations. a. M = log₁11²1 b.…

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Q: Consider the functions f, g, and h, which are differentiable for all x € R and h(x) − 2 #0 - for all…

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Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: equa 5 itions all approach y = 4 = 5 5 4 a - Y as t →∞. dt

A: Topic:- application of integration

Q: Question 8 of 25 > Find the derivative of the function f. 3 √x f(x) = O At

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Q: Find curl (62 i + 7x j + Sy k). curl (62 i +7x j + 5y k) = (i k )i + (i )j + (

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Q: y(t) = C₁ e-5t + c₂ e-6t

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Q: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

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Q: a)lim              (e^-x)(x^2+sinh(x+2))    x->∞   b) Find the point where the tangent to the…

A: find limit solve the parametric equation

Q: Prove that: V² (64) = $V²y +2V¢• Vy+yV² ¢

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Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: Given differential equation:- dNdt=N1-0.0008N , N(0)=1

Q: Find the volume of the solid formed by revolving the area bounded by the curve y^2 = (x^3)(1-x) in…

A: Given problem:- Find the volume of the solid formed by revolving the area bounded by the curve y2 =…

Q: A 10-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

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Q: Find the absolute extrema of the function   f(x,y)f(x,y) = 3x^2+3y^2+2x+2y−4   on the domain defined…

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Q: A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate,…

A: Solution: Car rented =480 -10x rate =20+x

Q: Rewrite the following 1. sin¹ (3x) = Submit Question as a sum of trigonometric functions with no…

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Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

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Q: O Question 9 Find f'(a) if f(x) = arctan(In z). 1 z (1+x²) 1 a sec²(In 2) 1 1+ (In 2)² 1+ 1 ()* 1…

A: To find the derivative of given function.

Q: For the function f(x,y)=−5x2+2xy+3y2−x−5y+1f(x,y)=-5x2+2xy+3y2-x-5y+1, find a unit tangent vector to…

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Q: 5- The table below shows the speed-time change of an athlete in a 20-minute running period. The…

A: Given, I=∫020v.dt The Simpson Method and the Trapezoidal Rule are used to complete the integration.…

Q: Find the polar equation for the Cartesian curve x² - y² = √√x² + y².

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Q: Use the formula к(t) = = k(t) = = ||r' (t) × r"(t)|| ||r'(t)||³ r(t) = t²i+t¹5j to find (t).

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Q: Evaluate the definite integral. [²³ sin5(x) dx Step 1 6.² sin5(x) dx, first rewrite the integral. To…

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Q: Imagine that you work as a designer in a company that designs baby bottles. Your mission is to…

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Q: 7. Choose the appropriate table for the differential equation X y ଶ୪ X y dx X Y -201 -4 1 2 2 -1 -1…

A: The solution is given below

Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

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