Evaluate the following limit using L'Hospital's rule. Provide your answer below: دی lim (4x) X18

Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

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Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: Graph the following function by using a convenient method. y = -3cos(30° - x/3)+ 7

A: This is a graph function

Q: 2. Use the following partial graph of f(x) to answer the next question. f (x)' 10. The value of (f…

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Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

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Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

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Q: Let f(x) = 2x³-7x² + 4x. a. On what interval(s) is f'(x) > 0? b. On what interval(s) is f(x)…

A: Given problem:- Let f(x) = 2x3 - 7x2 + 4x .   a. On what interval(s) is f'(x) > 0?   b. On what…

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Q: Calculate[r₁(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt the product directly and then…

A: r1=9ti+3t2j+8t3kr2=t4k

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A: This question is related to Cost and Revenue function, we will solve it using given information.

Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

A: Given query is to find the area under the curve.

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Find the period of y=-3cos(3.7x). Round your answer to 1 decimal place.

A: " Since you have asked multiple question we will solve first one for you. Please specify question…

Q: Calculate the line integral of F(x, y) = -4i + 5j along the line segment from (-3,-4) to (-5,0).…

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Q: Use one of the following three formulas for the area of the region enclosed by C 1 fxdy = f - ydx =…

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Q: 22// use the tests indicated in front of each of the series ollowing to determine if the series…

A: 1. Summation of (k+1)/(k2-1) from k=2 to infinity.  2. Summation of 1/(5k+1) from k=1 to infinity.

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Q: 42. If g(0) = 0 sin 0, find g"(π/6).

A: Solve the given

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Q: 3. Find an equation for the parabola with directrix at r = 3 and focus (-1,-1). Find the two latus…

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Q: The graph of a function f is given. Use the graph to estimate the following. y 5 (a) All the local…

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Q: n=5   Use taylor series to approxim. from the interval of: 0-1.5   e^(x^2)dx   Round to 4…

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Q: For two exclusive events A and B, P(A) = 0.2 and P(A U B) = 0.65 If the given information is shown…

A: Solved below

Q: f(x)=x√ 36 = x² ntercepts (x, y) = (x, y) = (x, y) = elative minimum (x, y) = elative maximum (x, y)…

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Q: n k=1 Note: Your answer should be in terms of n.

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Q: Solve the system using Cramer's Rule. - x + 2y = - 5 4x + 5y = 32 Find the determinant D…

A: D=-1245D=-1(5)-2(4)=-5-8D=-13Dx=-52-325Dx=-5(5)-2(-32)Dx=-25+64Dx=39Dy=-1-54-32Dy=(-1)(-32)-(-5)(4)D…

Q: ∞ -1. Σ(-1)" n=1 n! 2"

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: Solve the differential equation by separable variable

Q: I. Evaluate the following integrals by substitution. Show your complete solution 1. S (3x + 5)12dx…

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Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

Q: 8. If the graph of h(x) goes thro following statements are true fc

A: 8) y=h(x)g =h(x)This transformation only affects y-value.A(-16, 4)y(x=-16)=4, g(x=-16)=4 =2A' (-16,…

Q: Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Maximize z = 3x…

A: Here, the feasible region by the curves x+y≤1034x+y≤160y≥23x,y≥0 is:

Q: A person's weight increases with height through approximately the end of the teenage years. Dan's…

A: In this question ,we can find Dan's weight .

Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: y varies inversely as the fourth root of x and when x = 81, y = 10. What would be y when x=44. Round…

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Q: Investigate the given two parameter family of functions. Assume that a and b are positive. f) =…

A: We will plug the values of a and b to do the analysis.

Q: Below is the graph of a polynomial function with real coefficients . All local extrema of the…

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Q: St-1.0t vemos anoitasu) InemzeozeA B C E M N K JH G Identify each of the following in the figure…

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Q: [2 xe3 dư =

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Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 3 1 = lim t+oo 8t² +9' 5t, (?, ?)

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Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y&gt;0To find : Find the exact length of the curve.

Q: x²+x dx (x²+1)(x+2)

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Q: A company determines that its demand function is given by p(q) = -0.4q+ 1754 and that its cost…

A: p(q)=-0.4q+1754C(q)=62.97q+3515R(q)=1128000R(q)= q. p(q)R(q)=q (-0.4q+1754 )R(q)=-0.4q2+1754q

Q: Use Newton's method to approximate a root of the equation z + c + 3 - 0 as follows. Let I, = -1 be…

A: Let's find.

Q: Find the equation of the tangent line to the function y = xsin x when x = 6.

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Q: (a) [1.1] (b) [1.1] (c) [-0.1] (d) [-0.1] (e) [2.99] () [-2,99]

A: We have to find the value

Q: Solve me initial No need to Jimphiry. by value the separaion of variables a.

A: To solve the following initial value problems by the separation of variables.a y'=1+y2, y0=1b…