• L₁²*²1*²** LI Q16: 2z√x² + y² dz dy dx (Hint: use the cylindrical coordinate)

Q: Consider the following functions. f(x) Find (f + g)(x). = g(x) = Find the domain of (f + g)(x).…

A: Domain of a function y=f(x) is the set of values of x for which f(x) is defined.

Q: dy 15. Determine the derivative dx for y = 3 cos(8x+6) Show your work.

A: The function is given by y = 3cos8x+6 To evaluate: the expression of dydx.

Q: Given the non-homogeneous differential equation y "- 4y + 4y=e²x What is its auxiliary equation? 0…

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Q: Find the derivative of the function. y = sin ¹(cos ¹(t))

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Q: 3x 16x³ +24x² - 9. Find: 10. Given f(x) = a) All maximum and minimum points b) All intervals wher

A: given that ;- f(x)=3x4-16x3+24x2-9now ,  f'(x)=ddx3x4-16x3+24x2-9f'(x) = 12x3-48x2+48xand…

Q: Part b pls

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Q: d) xy' + (1+x)y=e* sin(2x)

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Q: Find dy/dx and dy/dx². x = e, y = te-t dy dx² For which values of t is the curve concave upward?…

A: Given query is to find indicated derivative.

Q: Differentiate the function. g'(x) = g(x) = In(xe−8x)

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Q: 5. Consider the polynomial graphed to the side. Answer the following questions using that function.…

A: We need to interpret the graph.

Q: Evaluate sin 5x cos 4x dx

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: (b) Given the graph of f (x) below (blue), select the correct graph of the transformation y = 2f (x)…

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Q: Use the summation formulas to rewrite the expression O O 4 8 71 72 6 8 6 S I I I + n 8 4 72 8 S…

A: 12+22+...+n2 = n(n+1)(2n+1)6. 1+2+...+n = n(n+1)2

Q: Work of 1 Joules is done in stretching a spring from its natural length to 11 cm beyond its natural…

A: Given: Work done, W = 1 Joule Strech of the spring, x=11 cm = 0.11m   Now, The spring constant is…

Q: Given the homogeneous differential equation: y (4) + 3y "- 4y=0 What is its auxiliary equation?…

A: Given that the homogeneous differential equation is y(4) + 3y" - 4y = 0 . Here we have to find its…

Q: Use geometry to evaluate the following integral. 5 frixe 1 f(x)dx, where f(x) = 2x if 1≤x≤2 6-2x if…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  first we need to…

Q: (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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Q: Consider the following curve. 1 + x 4 + ex Find y'(x). y'(x) = y = 1 Find an equation of the tangent…

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Q: Consider the integral [32² In(x) dx: Applying the integration by parts technique, let u and dv Then…

A: To evaluate the integral ∫3x2 lnx dx by using integration by parts technique.

Q: locity of 6. Find the average value of f(2x - 1)³dx.

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Q: (c) sin 13л 15 COS Зл 15 COS 13п 15 sin 3п 15 Answer: sin 10п 15 = sin (2) 3 2п √√3 =

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Q: U. Solve the given equation 1) sec x(2 sin x-√2)=0 T Answer: x==+2nk, 4 TT ak 3π x== +2 4

A: Given query is to find the solution of the expression.

Q: Given f(x) = 19x - 3| +2 25. f'(²-) = If f(x)=(√3x-2)5 then f'(9) = Given f(x) = sin(3x)² 26. f'() =

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Q: Find the area enclosed by the curve x = x = t² - 2t, y = √t and the y-axis.

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Q: If total costs for a commodity are given by  C(x) = 850 + 30x  and total revenues are given by  R(x)…

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Q: 2- Say whether each given sequence is an arithmetic sequence. Find the common difference and the…

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Q: Obtain the general solution of the D.E. y - 4y + 4y=e²x O 1 + y=c₂e²+ = x²e² O 1 2x y=₁₁²³² +₂²² + =…

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Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas f f(x) dx…

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Q: Let f(x) and g(x) be two functions that we know very little about. In fact, all we know is that…

A: Let fx and gx be two functions that we know very little about. In fact, all we know is that ∫12fx…

Q: Use area to evaluate the integral 7x • ! 0 dx = dx, b>0. ...

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

Q: Find the exact area of the surface x = 6t - 2t³, y = 6t², obtained by rotating the given curve about…

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Q: Differentiate. g'(0) = g(0) = eº (tan(0) — 0)

A: dexdx=ex  d(tanx)dx=sec2xd dx(a.b)=adbdx+bdadxgiven  g(θ)=eθ(tanθ-θ)

Q: Find the limit. 45x -5x² lim X-9 3-√x 45x -5x² lim X-9 3-√√x (Type an integer or a simplified…

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Q: Solve the following initial valuc problem using the method of Laplace transforms y" - 4y + 5y = 8c³;…

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Q: ← dy (a) Show that y* +x-6=0 is an implicit solution to dx Part 5 of 6 1 on the interval (-∞,6). 4y…

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Q: Determine the open intervals on which the graph of the function f(x)= x²+64 is concave upward or…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves y = y=0, x= 0…

A: To find:- Volume of solid genrated by curves y=43x+3,x=0,y=0,x=3 about x axis

Q: Find the area of the region bounded by the graphs of the equations y = x³ + x, x=2, y = 0. Round…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

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Q: for v= -1/2 cos (2x) where is -1/2 coming from? In the final answer, where does 1/4 come from?

A: Solution ⇒    Given function  ∫udv=∫x×sin⁡(2x)    here  u=xanddv=sin⁡(2x)…

Q: sin(2x) x y = if x = л, dx = 0.25 find the differential. Round your answer to three decimal places.

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Q: The farmer knows that the area of the rectangular enclosure must be at least 400 square meters. This…

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Q: Find the sum of the first 30 terms of the sequence. 3, 12, 21, 30, ... S30

A: given  3,12,21,30,.....the difference between numbers is 9we know that sum of nth term of a.p. is…

Q: A farmer plans to fence a rectangular pasture adjacent to a river (see the figure below). The…

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Q: 20) Explain the idea behind l'hospitals vule.

A: use an  example to understand the l hospital rule.

Q: If lim X-5 f(x)-8 X-4 lim f(x)= X-5 = 1, find lim f(x). X-5 (Type an integer or a simplified frac

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Q: 7. The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

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Q: 1. Given the equation y = -7cos(4x + 20), find the following: (write the answers here and on paper)…

A: To solve the following problem and find the following things

Q: So Lov (x + y) dy dx to polar coordinates. a. Convert the integral b. Evaluate this integral. Hint:…

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