f (x)= arcsin (x³)+ aretan (4x)

Q: Problem 8. If the focus of a parabola is at (0, 4), and the directrix is y=-4, write the equation of…

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Q: Determine the convergence or divergence of the series using any appropriate test from this chapter.…

A: This question can be solved using the concept of geometric series test and p series test for…

Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

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Q: and y=x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the solid…

A: Given :-region bounded by y=x2  ,  y=x+2revolving about the x-axisusing washer/disk…

Q: Find y' and then find the slope of the tangent line at (4, 1849). Round the slope and y-intercept to…

A: Explained below

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

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Q: Evaluate the defınite integral. i+e"j+t k)dt O el2 12-( - 1) + O el2 – 1 i+ (e-' – 1) j + k el2 – 1…

A: ∫01e12ti + e-t j + t kdt=e12t12i -e-t j + t22 k01=e12112i -e-1 j + 122 k-e12012i -e-0 j + 022…

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: Given query is to find the value of the integral.

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: from e'dv Ve4v -16

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Q: dy 1- y}

A: Given query is to find the value of the integral.

Q: If z = +3y, find the differential dz. dz =

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Q: Use the limit comparison test to determine if the series converges or diverges. 00 22) E 6n3/2 + 7n…

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Q: Use Laplace transforms to solve the following initial value problem S y( (t) – y(t) = 8 (t) y(0-) =…

A: We need to find out laplace transform of the initial value problem, which is described in step 2 .

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + = subject to x2 + y…

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Q: Step Solve for c. Use inverse trigonometric functions to find the value of c guaranteed by the Mean…

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Q: EXAMPLE 1: Consider the graph of the funetion f given below. Using the given graph, determine if the…

A: topic- continuity of a function

Q: f is just that e*-sin(x + y) + cos(x +y)] and = -e* sin(x + y) which if the ollowing is true Select…

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Q: III. In a particular very small region, the consumer price index, C, depends on the current value of…

A: Let's find.

Q: Maximum Oil Production It has been estimated that the total production of oil from a certain oil…

A: given : Total oil production T(t) = −1000(t + 11)e−0.1t + 11,000   Production at time t given by

Q: 1. For the curve x2y2 = 25 at (-1,-5), find the equation of the normal line.

A: The given curve is: x2y2=25 Differentiating it with respect to x: y22x+x22ydydx=0 at (-1,-5):…

Q: the comverg ence and divergene test 2n

A: To find the convergence of the series.

Q: (c) Use de Moivre's formula to write down a formula for all o words, give a formula for the complex…

A: answer is in next step

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 5 sec2 x dx -T/6

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Q: y = x/x, x = 4, and y = 0 ... Revolve the area of the shaded region about the x-axis. Using circular…

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Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

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Q: Find an explicit formula for an. 1 1 4'9' 1 1 14) 1, 16' 25

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Q: 0 in quadrant II, find the exact value of: 81 If sin 0= sin 0+ sin 0+ 6. (Type an exact answer using…

A: topic - trigonometric identities sin(a+b)=sin(a)cos(b)-cos(a)sin(b)

Q: The area bounded by y =3Vx and 2y =3x is revolved about the x-axis. Using cylindrical shell method,…

A: Solve the following

Q: 6. v(y) = In (y² – 8y – 1)

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Q: d Calculate ri(t) · r2(t)] and d ri(t) x r2(t)] first by differentiating dt' dt the product directly…

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Q: y = x and y = x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the…

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Q: Integrate the following problems. Show all your work. 9. S(10xt – 5x3 + 3x)dx

A: Please refer to the image below

Q: Using (sin x) = cos x and (cos x) = – sin r dr dr Show that # (cot x) = - csc² x dr

A: We need to show that ddx(cot x) = -csc2 x Given ddx(sin x) = cos x and ddx(cos x) = -sin x

Q: Biologists stocked a lake with 280 fish and estimated the carrying capacity (the maximal population…

A: We need to estimate the carrying capacity.

Q: A line is given by the equation y = x in rectangular coordinates. V3 Which of the following…

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Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

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Q: Radius and Interval of Convergence of a Power Series. 00 Determine the radius and interval of…

A: Solve the following

Q: .5 2. 2. dx =D dx- (6+z*) o o (x²+9)½ 's (x²+9)½

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Q: 3. Find the binomial series for (1+x)3 4. Use the result in problem 3 to give a power series…

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Q: TUTOR %3D for the function

A: The given equation is: 4x2+x3y+y2=6...(1) To find the slope, that is dydx, at Q(-1,2)

Q: 7 Determine the intgral

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Q: You and your best friend Janine decide to play a game. You are in a land of make believe where you…

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Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: alyze and sketch a graph of the function. Find any intercepts, relative extrema, and points of…

A: We are allow to solve one question and 3 subpart only at a time. If you want rest of solution please…

Q: (А) True B) False

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: 1) Find dy/dr by implicit differentiation. box answer tan (xy¯+y)= x

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Q: Determine the convergence or divergence of the series. (If you need to use co or -0o, enter INFINITY…

A: limn→∞ sech(n)=limn→∞ 2en+e-n=limn→∞ 2e∞+e-∞=limn→∞ 2∞+0=0limn→∞ sech(n)=0