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Q: Differentiate each function y=2sin^3 pie x

A: As we know that; The Chain Rule: fgx'=f'gx·g'x The Power Rule: ddxxn=nxn-1 From the given function; ...

Q: Evaluate the improper integral. 16 16 dy dx 0 o Vx + Vỹ 256 O A. (1- In 2) 3 64 O B. (1- In 2) 3 128

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Q: A hoist mechanism raises a crate with an acceleration (in m/s) a= 1+0.2t, where t is the time in sec...

A: Rate of change of velocity is called acceleration and rate of change of displacement is called veloc...

Q: For the function f(x,y) = e9xy, find fx and fy. fx = ? fy = ?

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Q: Prove the identity. V3 + tan(x) tan(x + ) - 1- V3 tan(x)

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Q: log5 (y? – y) + csc-1 CSC -3y ||

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Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its a...

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: Find p, q if f" f(x) dx – f(x) dx = S, f(x) dx. - (Give your answers as whole or exact numbers.) p =...

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Q: Find the first derivative f' and the original function ƒ. f"(x) = x³ - 16x + 4, f'(0) = 3, ƒ(0) = 2 ...

A: Solve the following

Q: 8 If f(x) dx = 37 and g(x) dx = 12, find %3D [2f(x) + 4g(x)] dx.

A: Given ∫08f(x)dx=37 and ∫08g(x)dx=12We have to find ∫08(2f(x)+4g(x))dx

Q: Consider the applet above. The graph in blue is y = f(x). Move the points to construct the slant asy...

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Q: How many unordered sets are there of two items chosen from eight?

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Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) y = ...

A: Given:- F(x) = x4+1 , x=-3, Δx=dx=0.01 To find:- Δy and dy

Q: the radios of a circle is increasing uniformly at the rate of 3 cm/s.Find the rate at which the area...

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Q: A population of 620 bacteria is introduced into a culture and grows in number according to the equat...

A: For finding the rate of population growing we have to diffrenciate the given function and put the gi...

Q: Consider the function f (x) = 3x² – 18x + 27. - What is the exact value of C in the interval 3, 3 + ...

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Q: 3. Find the equation of the tangent line to the graph of y at the point (1,0) given 2r² where r> 0. ...

A: Given that: xy+1x2=2x2+y

Q: dy dzy dx2 てスえ)

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Q: Sociologists model the spread of rumors using logistic equations. The key assumption is that at any ...

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Q: Use the Laws of logarithms to rewrite the expression 5 19 log z7 in a form with no logarithm of a pr...

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Q: (-00, -3) -3 (-3, -1) -1 (-1, 0) (0, 1) 1 (1, +00) f'x + und und f"x + und und + +

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Q: 22 4* 36 * 64 Use the given transformation to evaluate the integral, where where R is the interior o...

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Q: (153) (b) Let g(x) = 2***. Find gs"(x). II

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Q: if f''(x) = 0 an inflection point, what can be said aboutthe sign of  f'''(x)?

A: We have to fund the condition for f"' (x) for a inflection point  to happen.

Q: What is the First Derivative Test used for? Testing where a continuous function is differentiable. O...

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Q: 1 4. lim In csch 1– 2x

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Q: Use the trapezoidal rule to find A, using the indicated value of n. dx; n=8 3 X +1 .....

A: Please refer the attached image for complete solution. THANK YOU.

Q: If log2 (5x + 6) = 3, then r = You may enter the exact value or round to 4 decimal places.

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Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =...

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Q: Approximate the value of the integral by use of the trapezoidal rule, using n 8. 11 121-x dx

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Q: If, in a monopoly market, the demand for a product is p = 2100 x and the revenue is R = px, where x ...

A: Maximize revenue

Q: Approximate the value of the integral defined by the given set of points. dx 0. 1 4 6. 0.95 2.05 3.5...

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Q: Find the points on the graph of the function that are closest to the given point f(x) = x2 - 9, (0, ...

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Q: * 1 - xזrJ TX X.

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Q: Find the unit tangent of the following curve at the specified point. r(t) = 2ti + 1 · sin(2t)j+3 · c...

A: We have to find the unit tangent vector at t=pi/3

Q: 4) (y- xy?)dx + (x + x?y?)dy = 0 ; when y(1) = 1

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Q: Find the absolute maximum and minimum of the function f(x, y) = 3y – 2x2 , constrained to the region...

A:  f(x, y) = 3y – 2x2 , constrained to the region bounded by the parabola y=x2+x-1 and the line y=x.To...

Q: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer.) sin(...

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Q: The possible letters are d, l, n, t, and v, and we wish to form a four-letter sequence. Therefore, w...

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Q: Question 8 Discuss the relationship between differentiability and continuity in a short paragraph.

A: Continuity :- There are two types of functions; continuous and discontinuous. A Continuous is a func...

Q: Let u = u(x, y). Solve the PDE Upr = 0. Select one: u = f(y) + yg(x), where f and g are arbitrary fu...

A: u=u(x,y), then uxx=0

Q: Q.41 The value of the quantity P, where P = |xe*dx, is equal to Cate Sxe*dx, %3D

A: Given,            P=∫01xexdx

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do no...

A: Partial fraction decomposition is breaking the fraction 1/f(x) to A/g(x) and B/h(x)+.....

Q: If f(x) = 3 cos(x) 0 <x< 3r/4 evaluate the Riemann sum with n = 6, taking the sample points to be le...

A: Here we have to find Riemann sum left Endpoints

Q: f(x)=(6x+5)/(4x+5) f'(x)=? Show work

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Q: Evaluate the integral. -2 4y2 - 5y – 12 5y - 12 dy У(у + 2)(у — 3)

A: Given that integration and we solve this integration by using general formulas of integration. Here ...

Q: f(x)= 8x2ln x Find the intervals where​ f(x) is increasing or decreasing.

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Q: Points Approximate the value of the given integral by use of the trapezoidal rule, using the given v...

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Q: Find p, q if f f(x) dx + f6º f(x) dx = ["' f(x) dx. (Give your answers as whole or exact numbers.) p...

A: The value of p is 4 and q is 16.

Q: Starting with the graph of f(z) = 2", write the equation of the graph that results when: (a) f(x) is...

A: Given f(x)=2x