When can we say that a function or a graph has extrema (both minimum and maximum value)

Q: Find the most general antiderivative. dy A В c) 8 +C D

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Q: Set up the double integral that finds the volume of the solid under the surface z = 8x² + 3y over th...

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x...

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Q: Consider f(x) = 6.5x^5 - 3.7x^3 + 7x - 1.6. Using the given function, approximate f(2) by making use...

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Q: Solve the following incqualities

A: The given inequality is: x2>x3

Q: er the integral is improper. sin(x) 61 + x2 xp O proper O improper Explain your reasoning. (Select a...

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Q: x'dx 1. Integration by Parts f Vx4-5 dx 2. Algebraic Substitution f (x+2)vx+1 3. Trigonometric Subst...

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Q: Find all critical values and critical points of the function given, then find the regions where the ...

A: The answer is in step 2.

Q: ution 1- u? cos x and dx 1+ u? grand to a rational function of u, and t al. If you have a CAS, use i...

A: We have to find the indefinite integral according to the given information

Q: COS ydy

A: We have to calculate the given indefinite integral

Q: A radioactive substance has a half-life of 29 years. What percent remains 80 years after being to it...

A: We will find the remains after 80 years in percentage. 

Q: If f (x) =2x³+6xr- 2, then what is f'(1)? %3D

A: Solve the derivative of the function for given value

Q: Cosx Evaluate the Integral dx. sinx 1 + C 3sinx A B) 1 +C sinx - +C 3sinx 1 +C sinx

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Q: 1) An equilateral triangular plate with 6m side is submerged vertically in a tank of water so that i...

A: Here, the top surface of the triangle plate is 2m  below the free surface of the water. Therefore, ...

Q: Find the area of the region between the parabola y = 9 - x² and the x-axis. Round your answer to thr...

A: We can find the area as follows:

Q: 1. Find the value(s) of x that satisfy x? – 3.5x + 1.8 = 0.

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Q: The number of bacteria "N" present in a culture increases at a rate proportional to the number prese...

A: This question is based on application of differential equation.

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: Given :   f(x)=7sin(pix) X0=9/2

Q: ; find value of matrix A eigen -2 A = 2. 2.

A: To find the eigen value of the given matrix A , we have to evaluate the determinant of A-λI and then...

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A: Solution is written in below steps.

Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: Let ft)=F(t), where F (t) = 412– 5t²+ 5t¸ Evaluate the following integral using the Fundamental Theo...

A: As we know from the fundamental theorem of calculus; If F't=ft then, ∫abftdt=Ftab=Fb-Fa   From the g...

Q: Which of the following is NOT EQUAL to the given integral. tanx 4+x2+x4 tanx tanx dr 4+x2+x+ dx+ -2 ...

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Q: Evaluate the Integral tanh (u) du

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Q: n (x+1)] Evaluate the limit of the function f(x) = e of Values method. as x approaches 0 using Table

A: Solution is written in below steps.

Q: Assume that the following relationship is known to be true for two angles A and B: sin A cos B - cos...

A: The given relationship,     sinA cosB-cosA sinB=0.133599

Q: Evaluate the integral

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Q: State the trigonometric substitution you would use to find the indefinite integral. Do not integrate...

A: Here, to evaluate the given integral use the trigonometric substitution. ∫x2(x2-36)32dx

Q: 1. Use finite approximations to estimate the area under the graph of the function f (x) = x³ between...

A: The function fx=x3 between x=0 and x=1

Q: Find all critical values and critical points of the function given, then find the regions where the ...

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Q: Evaluate the Integral / tanh (u) du .

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Q: Find the coordinates of the centroid of the solid generated when region bounded by x2 + y2 – 2y = 0 ...

A: The given curves are: x2+y2-2y=0 y=2-x

Q: Find the function that is finally graphed after the following transformations are applied to the gra...

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Q: In (In y) dx + xy³ dx + x²y² dy+ In x dy = 0 y In y %3D 3.

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Q: Solve the following incqualities - 21 < 4 •

A: The given inequality is: 1x-2&lt;4

Q: SOLVE THE TRIGONOMETRIC EQUATION a. V3cosxcscx = 2cosx

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Find the integral. S 12:3 k dx x9/2 + C B x9/2 + C x9/2 + C 24 x9/2 + C A,

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Q: The number of bacteria in a culture is growing at a rate of 2500e2t/5 per unit time t. Find the numb...

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Q: Identify the method applicable and evaluate the integral using the identified method: adx 5. S - (a+...

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Q: For what value of the constant c is the function f(x) continuous at x = 1 Seter-2, | In (x) + 6, if ...

A: We will use concept of left hand limit and right hand limit in this problem.

Q: Find the indefinite integral using the substitution x = 8 sin 0. (Remember to use absolute values V6...

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Q: In order to give the complete solution of a nonhomogeneous linear differential equation, a particula...

A: Complete solution of a non homogeneous differential equation is given by as follow. 

Q: 2-x'y'y'+ xy' =1

A: Let's find. 

Q: If 8 cos (3x) < g(x) < 8 + 2x for all x. Find lim g(x)

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Q: Given two planes: 3x + 9y-4z = 0 and x + y- 5z = 8, determine the value of the angle between these t...

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Q: dx Perform the Integrations 1+ sin x+ cos x Use the editor to format your answer

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Q: What is the area under one crest of the sine curve, from x = O to x = n? y=sin x dx 1/2

A: Given problem:-

Q: Find the product z,z2 and the quotient 2. Express your answers in polar form. Z2 Z1 = (플) +i sin(플))...

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Q: Use finite approximations to estimate the area under the graph of the function f (X) = x³ between x ...

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Q: 2 Find fx) + 2g(x)]dxif / F(x)]dx = 5 and / [g(x)]dx - 3. 1) In order to evaluate this integral, use...

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