1. Consider the curve of the function f (x) = 2x² a. Find an expression for the slope of the curve at any point x.

Q: 3 Determine the equation in the form f(x)%3= for the function with a vertical kx - c asymptote at x ...

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Q: - 1) ? du

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Q: d?y (2) dx2 2dy + 4y = 0 No boundary conditions

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Q: 8. y = In(x + V +1)

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Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the direc...

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Q: dx Evaluate Зх — 12 A 00 B + 00 1

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Q: Find r²e* dx.

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: 10* -dx may be written as Aln secB*+ tanB*|+ C, where A, B, and C are constants not equal to zero. E...

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Q: Using calculus, find the volume of the solid defined by 1<r< 3,0 <osT/2 and 0 < O ST.

A: The objective of the question is determine the volume of the solid at given region.

Q: 10 -dx may be written as Aln|secB"+ tanB"| + c where A, B, and C are constants not equal to zero. Ev...

A: The given integral,         ∫10xcos 10xdx

Q: A particle moves in a straight line according to a law of motion s = f (t), t>0, v %3D in seconds an...

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Q: Find the dimensions of a rectangular lot with perimeter of 300m and whose area is maximum. Use Opti...

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Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4. O 21/2 square ...

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Q: Find dy/dx of the following functions. A. y = x⁵tan5x B. y = esec2x

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Q: Cost and Revenue functions C(q)=q3−11q2+55q+5000 and R(q)=−3q2+2500q​, what is the minimum marginal​...

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Q: 3. Solve for x: (3)*+1 = V3

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Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: vas y dS

A: Use simple integration formula.

Q: I. Solve the following: 1. Given: y = 2x - Find: a.) dy/dx b.)y" 2. Given: 16y – 9x? = 144, find y" ...

A: Given  1. y=2x-13+43x-2 if x=22. 3x+4y3=5 If (3,2) To find slope m:

Q: sin-cos-sino d®? 2 2 What is the integrable form of 2- 1 du B 2 | cosu du 1-u² du O -2/- D sinu du A

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Q: m m n т +n b. E k i) k - i=0

A: Please see the below picture for detailed solution. 

Q: Determine the convergence or divergence of the following series. 1 (a) Σ (Use Integral Test.) n(ln n...

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

Q: S(3x* – 5xP +x=³)dx.

A: Given query is to find the integral.

Q: Find all critical points of the function f(x) = x-15 – x-16. (Use symbolic notation and fractions wh...

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Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal...

A: Given,           A function is defined by the equation y=3x+4 and the slope of the tangent line     ...

Q: dx For -= In(F (x))+C. What is F (/3) if C=0? (x+x³) (xtan-(x)+1) -1 + - 3 1 + -1 + -

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Q: 3. Which of the following is an improper integral? -dr -4 x²–x- 2 А. In3e COSX хе 'dr В. dx c. 2x+ 8...

A: Given problem:-

Q: Substitution Method (15) (x² – y²) - xy = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 2x 5х-3 + 3x 12 2. 4x2 – 16 > 0 (-0, 2], [2, c∞0)

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Q: uestion 13 d +=x² +C. n P a b ze general antiderivative of (3x²-4)²x² can be written as m hat is the...

A: We are asked to find the antiderivative of the general.

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: Question 5 dx - = In[F(x)]+C.What is F(3) if C= 0? For (x+x*) (x Tan-lx +1) 1 A B 3 1 D

A: Integration is the act of bringing together small components into a single systems that functions as...

Q: Evaluate the integral: ſo (x³ – 5æ + 7)dx. Select one: O None. 19

A: Given :∫01(x3-5x+7)dx

Q: Consider the function fix) - sin x. Complete the table below and sketch its graph. 011/6 11/2 Sn/6 7...

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Q: ·sec-x)" sec'x 23. What should be the value of A for -dx to be integrable using the formula | u" du?...

A: the integration of the integral is (2-sec2x) eln(pi/e)sec3x/Sec(3A-x).

Q: 3x dx 1. S 2x 4-1

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Q: 3. The surface of an island is defined by the function z = e-(x<+y²)/8 – e-2 over the region on whic...

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Q: Question 16 In (ale) (2-sec2x)emlesec'x sec( 3A – x) What should be the value of A for dx to be inte...

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Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

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Q: Solve the initial value problems. 2. 2y" – 9y' + 9y = e3* y(0) = 0, y'(0) = - 8

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Q: d?y =6-9x and which passes through the points (0, -1) and (2, 3). Find the equation of the curve for...

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Q: cos2x – sin2x cos2x For What is F(x)? - dx=÷F( 3 + C• cosx – sinx O (cscx – secx) 3 2 sinx - -cos'x ...

A: Solved below

Q: sinx sinx +x cosx - e +e The integral / dx may be written as me"sinx + px + qe* + C. where m, n, p, ...

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Q: What is the integrable form of sin-cos-sin0 de? 2 2

A: A detailed solution is given below.

Q: Find the diameter of the of the circle with center at (-5, 3) and tangent to the line 8 – 2x = 2. 2 ...

A: Solution: center (h,k) = (-5,3) tangent to the line x-axis 8-2x=2 so, x= 3 &amp;y=0 (3,0)

Q: 1. y= x - x'cosx + 2xsinx + 2cosx

A: solution:-(1)y=x3-x2cosx+2xsinx+2cosxy'=ddxx3-x2ddxcosx+cosxddxx2+2xddxsinx+sinxddxx+2ddxcosx=3x2-x2...

Q: II Solve the ff. problems using trigonometric or inverse trigonometric functions Show illustration, ...

A: Let's find. 

Q: Which of the following is an improper integral? In(x++1) dr -1 dx -4 x2-x- 2 dx 2x + 8 In3e COsx xe ...

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Q: Use the Integral Test to determine if the series 1 Σ (n +2)°/¾ n=1 converges or diverges.

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Q: Consider the function fix) - sin x. Complete the table below and sketch its graph. 011/6 11/2 Sn/6 7...

A: Solved below