If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of the triangle changing when the sides are 12 meters?

Q: he function f(x) = xe" has one critical point. Find and classify it. (x) has v at the critical point…

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Q: Calculate the value of cos8π° using two terms of the appropriate series. Compare with the value…

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Q: Determine the radius of convergence of the following power series. Then test the endpoints to…

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Q: Let f(x) = ln(x7) f'(x) = ƒ' (e²) =

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Q: Let L(c) be the length of the parabola f(x)=x² from x = 0 to x=c, where c20 is a constant. a. Find…

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Q: Solve the following equations:* y" - 3y' + 2y = 2x² + ex + 2xe* +4e³x

A: answer is in next step

Q: :- 2)³. (2x + 1)* if y= 2x. 3x+8 dy Use logarithmic differentiation. Find dx

A: We know that power rule of derivatives is given as - d(xn)/dx = nxn-1.     Here i attached the…

Q: Find the length of the arc formed by ² = 10y³ from point A to point B, where A = (0,0) and B = (100,…

A: We can find the length of arc by applying length of arc formula.

Q: Verify that af ?x || 224 ?х ду = 224 ду дх - for f(x, y) = 7x®y³ – 5x5y4.

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Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: Find all the second order partial derivatives of g(x,y) = x+y+ 3 sin (y) + 4y cos (x). a²g n

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Q: Find the area under the curve using intervals of 1 unit (X) each Integral - Area Under the Curve…

A: Reimann sum:Take the left point of sub-interval:∫16f(x) dx =∑i=1N f(xi*) ∆x∆x=1∫16f(x)…

Q: The graph of the equation x2/3 +y2/3=52/3 is one of a family of curves called astroids because of…

A: solution:-equation of curveastroid x2/3+y2/3=52/3the length of half the first-quadrant portion…

Q: Evaluate the definite integral. 5 4u [(-*--*--* du (u + 3)² 4 5 1 ((---)-D 4u du (u+3)²2 4 (Type an…

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Q: 87元 6 2 23 4元 3 ✈0 江 11元 6

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Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

Q: y = 2', y= 3z, about the line x = 3 can be computed using the method of washers via an integral V =…

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Q: Q6: Solve Nhe Complex equation a, z+z + Iti = 0 3 b. Z°+ z+ Z +1 = 0 where Z= x

A: Concept: Complex numbers: A complicated equation is one that requires the use of complex numbers to…

Q: A population doubles every 24 years. Assuming exponential growth find the following: % help…

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Q: Father of Calculus Isaac Newton and Gottfried Wilhelm Leibniz Hipparchus of Nicaea Antoine Lavoisier…

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Q: Find the area of the surface obtained by rotating the curve y=1+3x² from x = 0 to x = 9 about the…

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Q: s, e -0.4 is

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Q: -7x - 2 y =-13 x – 2y = 11

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Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

A: We should recognise the t and do the appropriate calculations.

Q: The first derivative of the function y = 3x cannot be solved using implicit differentiation. Select…

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Q: Calculate the fluid force on one side of the plate using the coordinate system shown below. Assume…

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Q: Solve each of the following problems completely. Draw the complete figures for each question. 2.…

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Q: Find f, f, f. fx= f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

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Q: Find the differential dy of the given function. y = √√√√9-x²

A: Given y=9-x2 we need to find dy

Q: Use the graph of g(x) to answer each question. O

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Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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Q: The functions f, g, and h are defined as follows. f(x) = −3+√x+19 g(x)=−3 |x-8| Find f(-3), g(6),…

A: Topic:- function

Q: 5. For z=x2siny show that 332 332 = дудхду дугдх

A: Topic = Derivative

Q: 6 Consider the series n2 +n a. The general formula for the sum of the first n terms is S Your answer…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y=2x + 1 and…

A: find intersection

Q: The entire graph of the function g is shown in the figure below. Write the domain and range of g as…

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Q: The instantaneous velocity of a particle is defined as the derivative of some functions. Select one:…

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Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

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Q: Let f(x) = ln(x² + 2x + 3) f'(x) =

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Q: For the function f(x): - 3x + 10, evaluate and simplify the difference quotient. Question Help:…

A: The difference quotient of a function f(x) is given by, f(x+h)-f(x)h

Q: Let f(x) =x' - 7x² +2. Find (f")'(-4)

A: We know that  f-1'(a) = 1f'f-1(a)

Q: Given cost and revenue functions and C(q) = 117q+44000 and R(q) = -3q² + 2700q, how many items must…

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Q: 4) A spherical scoop of vanilla ice cream sits on top of a waffle cone. The diameter of the ice…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

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Q: The function f(x) = −2x³+3x²+36x has two critical points, c₁ and c₂. Find them and use the second…

A: We need to find and classify critical points.

Q: Determine the indefinite integral. 25 dx x In 7x 25 S= Sx157x x In 7x dx =

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Q: Given cost and price (demand) functions C(q) = 150q+46,400 and p(q) = -2.4q+880, if the company sets…

A: Given that cost and price (demand) function C(q)=150q+46,400 and p(q)=-2.4q+880.Also, if the company…

Q: Given cost and revenue functions and C(q) = 115q + 31000 and R(q) = -3q² +2500q, how many items must…

A: Let's find how many items must be the company produce and sell to break down.

Q: 2-]x³.e* dx 3- S x².cosx dx

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