Evaluate the following limit using L'Hospital's rule. Enter an exact answer. Provide your answer below: In(x³) lim x →∞ √2x+5 = In (x³) lim x→∞ √2x+5

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A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

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A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…

Q: [18x² √6x³ +5 dx 3 ○a. — (6׳ +5)³/4 + C b. (6x³ +54/5 + Oc.5(6x³+5)¹/5 + C d. 5 Od (6x³+5) ³/4 + C…

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Q: Solve the given equation in the interval [0,2 π]. Note: The answer must be written as a multiple of…

A: This question can be solved using the concept of solution of trigonometric equations.

Q: Evaluate: sec²(4t) [3-tan(4t)]³ dt a.-16 [3-tan(4t)] + C b. | [3 –tan(4t)] + C 4 OC. 1 [3-tan(4t)]…

A: integration

Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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Q: Evaluate the following integrals. 2. √x* +5x³+ x+5x³+20x+16 x(x²+4)² dx

A: Solving

Q: Given: X == In(x²y - 1) y Find dy/dx. dy dx x²y-1 y-1 (E) None of these 1 2xy dy y x²y-1 dx + dy dx…

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Q: the slope intercept equation of a line that passes through (0,-6) and (3,-4) is

A: Given points are (0,-6) and (3,-4)and here (0,-6) is (x1,y1) and (3,-4) is (x2,y2)We know the slope…

Q: 9. (y³+4)√1- cos² (y4 + 16y) ». f (y ³. cos(y¹+ 16y) () 2. dy

A: Answer of the above integration is

Q: QUESTION 12 dz State the multi-variable chain rule for if ди z=z(t. s, w), t=t(u, v), s=s(u, v), w=w…

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Q: using an online graphing app, construct three graphs which lie on the interval (-8,8) choose three…

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Q: Evaluate the iterated integral. (x + y²) dx dy THERE

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Q: 10. x*(lnx + 1)8** dx

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Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: It meets the x axis in A and B respectively and y axis in D and E respectively.To Find: Family of…

Q: Find the limit. NOTE: Enter the answer using round brackets. 1 lim (12²2 +9.7) = (17.00) 9't

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Q: Question 7 Find the area enclosed by the curves y=2x², y=2√x,x= — and x = 1 A 45/51 B) 59/76 49/96…

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Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

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Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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Q: 1. y = 3x? – 2x4 - 3x3 + − − 2x + 1; y(4) - 8

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Q: y = x² + 2, y = 2x + 5, x=0, x=6

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Q: Determine whether the improper integral diverges or converges. 00 √x³²e-x dx O diverges Evaluate the…

A: To find the integral: ∫0∞x2e-xdx converges or diverges.

Q: 1. Consider the graph of f shown below. Using geometry (areas of rectangles and triangles),…

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Q: 1. What rule is applied in the following given? * Dx (-13) = 0 Power Rule of Differentiation Product…

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Q: Find each limit, if it exists. (a) 6 - 7x lim x-00 6x³2 (b) 6-7x lim x→∞ 6x-2 6-7x2 (c) lim 6x - 2…

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Q: [CLO-2] f(x) and g(x) are functions that are continuous on the interval -3 ≤x≤2 and satisfy 1 1…

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Q: Write the conjugate of √a +3

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Q: Find the​ consumers' surplus at a price level of p=​$150 for the​ price-demand equation below.…

A: Recall:  Consumer surplus=∫0x(D(x)-p)dx Given, p=​$150 p=​D(x)=300−0.05x

Q: Find the arc length L of the graph of r(t). r(t) t L= = ³²³i + 1 j + 1/2 √√61² k, 25157 = i

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Q: Find the value(s) of k such that the function x≤ 2 (x³ + k x³-8 f(x) = x > 2 ) x-2 is continuous at…

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Q: Find the present value of a $30, 000 annual income stream if it is invested immediately as it is…

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Q: The function f is defined as follows. 2x if -2<x<0 f(x) = x³ if x20 (a) Find the domain of the…

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Q: Activity 4: Determine whether the functions below are continuous or not on a given point or a given…

A: A function f(x) is continuous at a given point x=a   if following conditions are hold: (I)…

Q: 5-39+370=?

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Q: y Given: xe² + In(x - y) = . Find dy/dx. dy 2x(x-y)-x¹+x -w) (20

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Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Consider a triangle ABC like the one below. Suppose that b=58, c=34, and B= 108°. (The figure is not…

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Q: 25 2 la

A: We have to find the following conditions according to the given information

Q: Find a, and d for each arithmetic series. See Example 8. wwwww 62. S31 61, S20 1090, 920 = 102 64.…

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Q: 21 te 1 1 1-2 1-2 None of the alternatives are correct If L <=lim In p-400 then f(t) is 0+2

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Q: Given the function f(x) = 3x - 7, evaluate and simplify the expressions below. See special…

A: The function is given by fx = 3x-7 To evaluate: The values of fa, fa+h and fa+h-fah

Q: approximate with accuracy 10^3 to the solution of x³+x-4 = 0, lying in the interval [1,4].

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Q: y = (1 - √√x)³; y(3)

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Q: Determine whether the improper integral diverges or converges. 4 00 1.00 cos(7x) dx 10 O converges…

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Q: Given the expression below, set up (DO NOT SOLVE) the partial fraction decomposition. (Use A, B, C,…

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Q: 2x²+x-1 Evaluate -dx using method of partial fractions. Which of the (x-1) (x³+1) following is the…

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Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: owin - y" −4y' +4y=0 L".

A: 1)  y''-4y'+4y=0 Auxillary equation is m2-4m+4=0m2-2m-2m+4=0m(m-2)-2(m-2)=0(m-2)2=0 ⇒m=2,2

Q: Evaluate the iterated integral. LP'&x+yaxay (x + y²) dx dy

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