A chemical factory tank stores an amount of liquid. After it has started to drain, it has a given equation of = 100(- 20)2 in liters and refers to the time in minutes. At what rate is the liquid running out at the end of 6 minutes?

Q: Evaluate the limit In(x) lim x+1 x- 15x+ 14

A: Given,  limx→1ln(x)x2-15x+14

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Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

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Q: Determine the local maximum and minimum values and the saddle points of the function: f(x,y)…

A: Given, f(x,y) = y3 + 3x2y - 6x2 - 6y2 + 2

Q: Write an equation for the polynomial graphed below 5 4 3 1 2 -1 -1 2 3 4 5 -5 -4 -2 - -3 -4 -5 +…

A: topic- polynomials

Q: Find the simplified difference quotient. f(x) = 2x +6

A: answer is in next step

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

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Q: Find the Average Rate of Change of the following function ver the interval [1, 7] (That is, from t=…

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Q: Write a in the form a = a-T+anN at the given value of t without finding Tand N. r(t) = (2t + 3)i +…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: A tire swing attached to a tree branch swings with an arc length of 40 feet on its first swing. On…

A: Question- A tire swing attached to a tree branch swings with an arc length of 40 feet on its first…

Q: 5+ 4. 2 1+ -5 -4 /-3 -2\1 1 5 -1 -2 -3 -4 -5 + 3.

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Q: Use implicit differentiation to find the slope of the tangent line to the curve x3 + 9 2y - 10 at…

A: Topic:- application of derivatives

Q: Qu 1 a). Determine the LaPlace transform of the differential equation y"- y = e2 ; y(0) =0 and y"(0)…

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Q: thế föllowing triangle. (bebaon as Boosla Iamiab A = 31° B= 29° C = 14 m Select the correct choice…

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Q: dy given the dx Use implicit differentiation to determine equation x? + y² = 4. dy dx

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Q: Sketch the region enclosed by 2y = 5/a, y = 4, and 2y + 2æ = 7. Decide whether to integrate with…

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Q: 9. Find the vertical and horizontal asymptotes of the function. X-8 f(x): х2 — х — 6

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Q: 18. Find [ 2x°(2x* -1) dx

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Q: In the appropriate interval of convergence, we know that then we %3D 1. 1 can deduce, by applying…

A: We have to find to check the correct

Q: f'(x) =-+e²* +x²and f(1)=. Find f(x) Given

A: Here, given that: f'(x)=1x+e2x+x3⇒f(x)=∫1x+e2x+x3dx+C⇒f(x)=∫1xdx+∫e2xdx+∫x3dx+C⇒f(x)=ln…

Q: Write the function below in the form y = f(u) and u = g(x). Then find as a function of x. %3D y = V…

A: Given:        y  = 3x2-4x+2

Q: Refer to the figure below to find the limit lim f(x). X - 00 3.5- 2.5- 1.5- 1- 0.5- 2.

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Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

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Q: Find the number(s) b such that the average value of f(x) = 6x? 42x + 70 on the interval (0, 6 is…

A: The average value of f(x) in the interval a,b is given by, 1(b-a)∫abf(x)dx

Q: Use the graph of the function f shown to the right to estimate the indicated function values and…

A: topic- limits

Q: Find each function value and limit. Use -∞ or co where appropriate. 7x* - 14x2 f(x) = 8x° +4 (A) f(-…

A: topic- functions and limits

Q: 2 v2x-x2 XY xydydx 0 0

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Q: 4. Determine the equation of the plane passing through the point (1,-4, 3) and parallel to the plane…

A: Explanation of the answer is as follows

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Q: Write the composed trigonometric function sin (arctan x)sin (arctan x) in terms of x. Explain your…

A: In this question we have to find the function in terms of x.

Q: dy without first solving for y. dx e implicit differentiation to find ² + 3x + xy = 100 the given…

A: Topic:-  application of derivatives

Q: Bolyng bernoulli differential equation

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Q: Solve cos (w) - 6 sin(w) for all solutions 0 < w < 27 %3D w = Give your answers accurate to 2…

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Q: Evaluate the integral |- 5x + x3 - 2 x5 dx 3

A: Topic:- integration

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

Q: A = (Round to thế heares There is no solution. e the value of a. Select the correct choice below…

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Q: x = 2 + 5 cos t Consider the parametric equations for 0stsa. y = 8 sin t

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Q: Write a in the form a = a-T+a,N at the given value of t without finding Tand N. r(t) = (3e'cos t)i+…

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Q: y =1+6.x% Osrsl for Find the exact length of the curve

A: Length of the curve

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A: Given : h(t) = 2t2-6 (cm)              r(t) = 8-t2 (cm)                t= 2 sec

Q: Construct a table and find the indicated limit. Vx +2 If h(x)= x-8 then find lim h(x). x-8 Complete…

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