Evaluate the limit using L'Hopital's rule 6 cos(7x)sec( – 3x) lim x →

Q: Find the solution to the differential equation shown: y" - 2y' + y = x² - 1; y = 7 and y' = 15 when…

A: Given differential equation, y''-2y'+y=x2-1, with initial conditionas as y0=7, y'0=15, We need to…

Q: Given an interest rate of 1.0% compounded continuously and starting principal of $5000, determine…

A: Continuous Compounding Formula: A = P·er·t where A is the Accumulated Amount. P is the Principal…

Q: Consider the function y= x Find y'.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find all second order derivatives for z = 7ye5x Zxx Zyy = Zxy=Zyx = |

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Q: Given four points A(-6,-5), B(4,b), D(5,5) and E(3,7). The straight line AE cuts the y-axis at C and…

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Q: 3. The equation of motion of an object is given by s(t) = tet, where 0 ≤ t ≤ 10. Find the…

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Q: Which of the following is a second order linear differential equation? *

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Q: Use the transformation u = y-x, v=y to set up a double integral necessary to evaluate SS R on the…

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Q: Given an interest rate of 5.5% compounded daily (ie: compounded on each calendar day), determine the…

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Q: Find the radius of convergence of the Maclaurin series for the function below. f(x) = tan ¹(2x)

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Q: Use the table below to find X f'(x) g'(x) 1 2 1 [1.3f(x)] |x = 5 = 253 1 [1.3f(x)] dx 3 4 1 2 لی اند…

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Q: Anika and Barry drive go karts, east and south, respectively. Starting from the same place at the…

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Q: Find the general solution of the differential equation: dy 2ty + 4e-t². d.t What is the integrating…

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Q: Rewrite the given iterated integral using cylindrical coordinates. Do not evaluate the integral. 3…

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Q: In a figure, OABC is a parallelogram. Prove by the analytic approach that OB2+AC2=2(OA2+OC2).

A: Concept: Pythagoras theorem states that sum of the squares of perpendicular and base is equal to…

Q: 8 A communication signal is given by the function sint t The task is to: y=- a) Derive and equation…

A: To find the derivative of given function

Q: Enter a letter and a number for each formula below so as to define a continuous function. The letter…

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Q: An open-top rectangular box is being constructed to hold a volume of 300 in³. The base of the box is…

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Q: Let f(x, y) = x² + 2y¹ + 40xy. List the critical points: The critical point at the origin is a…

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Q: the absolute extrema if they exist, as well as all values of x where they occur, for the www ect the…

A: Topic:- application of derivatives

Q: Find the limit. lim x→∞ 5x + x³ + x5 1x² + x4

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Q: By Lagrange find √18 where √√16=4,√√25 = 5, 4.5 O 38 O 9 18 O 9 40

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Q: that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find…

A: Given query is to apply rolle's theorem.

Q: F(x) = F'(x)= = 2x 1,²² t² t² + 1 dt

A: Given query is to find the derivative.

Q: 162. y² = 4x For the following exercises, convert the polar equation to rectangular form. 163. r 4…

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Q: Question1: a) Find a power series representation of 1/(3-2x). b) Find a power series…

A: (a) Given that , fx=13-2x Find a power series representation of fx.

Q: Suppose that f(x, y) = 2x + 4y at which −3 ≤ x ≤ 3, − 3 ≤ y ≤ 3. Absolute minimum of f(x, y) is…

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Q: In order to find the area of an ellipse, we may make use of the idea of transformations and our…

A: The region R is bounded by the ellipse:(x-4)216+(y-2)21=1

Q: Perform scaling on a triangle (1, 1), (8, 1) and (1, 9) with a scaling factor of 2 in both x and…

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Q: Find the value of dx ∞ L 2 (2x 2)8 Determine whether 1 Σ n=2 (2n - 2)8 is a convergent series. Enter…

A: Given query is to find integral converging or diverging.

Q: Find the values of x, y and z that correspond to the critical point of the function: z = f(x, y) =…

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Q: Express the given equations in polar equations. x² + y² = 7 4xy = 3 (a) (b)

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Q: Evaluate the integral. 3 π 4л SS S y cos z dx dy dz 0 0 0 3 π 4л S S S y C 0 0 0 y cos z dx dy dz=

A: The given triple integral is y cosz, x fron 0 to 4pi, y from 0 to pi, z from 0 to 3.

Q: Find the points on the cone z² = x² + y² that are closest to the point (1, 5, 0). Please show your…

A: Consider A(x,y,z) to represent the point on cone z2=x2+y2---(1)The distance between (1,5,0) and…

Q: Which of the following functions (there may be more than one) are particular solutions to the…

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Q: Which of the following differential equations most likely represents the given directional field? a.…

A: The answer is in step 2.

Q: 50 40- 30 20 10- -10 1.0 10 20 30 40 Akilah is a lifeguard and spots a drowning child 40 meters…

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Q: 4x² - y² 5 (-1, -3) that has a positive a component. For the function f(x, y) = 3 find a unit…

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Q: The following table shows the average life expectancies in several countries. Assume that all…

A: The following table shows the average life expectancy in several countries. Assume that all premiums…

Q: xx): 1 + x² For what value of c is f a probability density function? C = For that value of c, find…

A: solution is given below.

Q: Use the root test to determine if the following series converges or diverges. 16 Σ n=1 (6+(1/n))²n…

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Q: K Find the area between y = 11xex and the x-axis from x = 0 to x = 1. The area is square units. ***

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Q: How many virus cells will be produced over the first two hours after the time of infection? (over…

A: We are given,  Rate of the virus, dV/dt = 150 * 2t - 30 Therefore, at any time t, the number of…

Q: Solve the following Differential equations: 1- (x²-yx²)dy + (y² + x²y²)dx = 0

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Q: For an interest rate of 10% per year, compounded quarterly, find the semiannual effective interest…

A: Given query is to find semiannual interest rate.

Q: You and your friend are shopping at the the nearby Target store. You spent 78 dollars on 3 pounds of…

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Q: Find  dy dx and  d2y dx2. x = et,    y = te−t

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Q: Find all the critical points of the function and determine whether each critical point is a local…

A: given function: fx,y=x3-3x+3xy2.

Q: Let - 20x² - 2xy + 6y² - 106x - 46y - 72 = 0. dy dx Use partial derivatives to calculate dy da at…

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Q: Find fx(x,y) and fy (x,y). Then, find fx (-1,2) and fy (3,1). f(x,y) = In 1+4x³y²| {x(x,y)= fy(x,y)…

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