Solve the problems. Show illustration. 1.A closed box, with a rectangular base,whose length is twice its width,is to have a surface of 192 sq. in. Find the dimensions of the box when its volume is a maximum. 2.Find the coordinates of the point/s on the curvey=2x2 which are closest to the point ( 9, 0 ).

Q: B. Evaluate the following lim 1. lim log x

A: Given: limx→12logx

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Q: 19 please

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Q: 3) lim x2-4 x-2 x-2 2- 2+ f(x) f(x) 1.5 2.5 1.9 2.1 1.99 2.01 1.999 2.001 1.9999 2.0001

A: This question is based on Limits.

Q: e+ = e2a-y C = e? 1 C = - O Option 4 Option 2 C =-e

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Q: 4) lim 12x – 1| x--2 -2- -2+ f(x) f(x) -2.5 -1.5 -2.1 -1.9 -2.01 -1.99 -2.001 -1.999 -2.0001 -1.9999

A: 4)limx→-22x-1

Q: lim (x*- 2x2-3)*

A: Let L is the value of given Limit.

Q: 4 -2 2. a

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Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. 1...

A: Let's find. 

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A: The medicare tax is 1.45%.

Q: Find the value of c when f' (c) = 0 for f(x) = 3x² – 12x + 9,where 0 <x< 4

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Q: dy y(ln y - In x+1) | da

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Q: 1. lim 5.54

A: To evaluate:limx→ c5.54

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A: We need to find equations of tangent lines.

Q: 1. (3x°y + 4xy' + 6}dx + (x + 6x°y° -1}dy=

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Q: Find the radius of the sphere x2 + y? + z? – 2x – 8 = 0. %3D 4 O 2 O 3 9,

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Q: 1 + d y 1 Suppose y = evaluate- 3 x-) x+1 dx

A: We will evaluate d3ydx3the given function y=1x-1+1x+1 in the following step.

Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

Q: EXERCISE 2.3.6 Let f(x) = x and g(x) = 11r. Find Dlf(x) +g(x)]. %3D EXERCISE 2.3.7 Find D (x6-7x5 + ...

A: Given that:                                  6. f(x)=x-4 and g(x)=11x37. Dx(x6-7x5+13)8. f(x)=-9x2  ...

Q: Find the limit. Enter DNE if the limit does not exist. lim (z,y) → (0,0) z2 + 15y2 Question Help: Me...

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Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed tri...

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Q: Given the following properties of a hyperbola, sketch the graph. State the complete properties: type...

A: Given the following properties of a hyperbola, sketch the graph. State the complete properties: type...

Q: dy Find in simplest form in each of the following dx - 5 1. y = - x³ – 4x² + 7x – 5 in

A: Given that: y=-5x3-4x2+7x-5     NOTE: As per our answering guidelines, we can only answer 1 question...

Q: Given that lim f(x) = 0 lim g(x) = 0 lim h(x) = 1 Xa lim p(x) = ∞ lim q(x) = ∞, evaluate the limits ...

A: We have to find the given limits.

Q: sinx 4. lim X0 sin nx

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Q: Compute the partial sums S3, S4, and S5 for the series and then find its sum. 1 n + 3 1 n + 2 n=1 (U...

A: The given series is  ∑n=1∞ 1n+2-1n+3

Q: Use the limit comparison test to determine whether the series converges. 00 4 5k + 5 k=1

A: Given that: ∑k=1∞45k+5

Q: Find the cosine of the angle between the two vectors: and Show all your work on your own paper; le...

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Q: The differential equation 3y(x -1dx+(x³ +8y– 3xdy = 0; is exact because OM ON %3D

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Q: Find DE using variable separable cos/dx + 1/ydy=0

A: Given that: cosxdx+1ydy=0

Q: 2004, an art collector paid $131,939,000 for a particular painting. The same painting sold for $26,0...

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Q: 1) lim (2x – 3) = 1 x-2 2) lim|x| = 0 x²-9 3) lim х-з х-3 9 3

A: 1)limx→2(2x-3)=1read : limit x tends to 2, (2x-3) is 1proof:limx→2(2x-3)=2(2)-3

Q: O sechudu = 2tan e" + C/ = tan (sinhu)+C -1

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Q: y = 2xy – x In(2y – 1) = –a² +C y = e**C + • Option 2 Option 3 In(2y + 1) = –x² + C Option 4 None of...

A: We need to choose correct option.

Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 | i...

A: Given query is to find the value of a and b.

Q: The revenue equation (in hundreds of millions of dollars) for barley production in a certain country...

A: If R (x) is the revenue function then R'(x) is the marginal revenue function.

Q: Hx'+y°-4x+Dy = - 2

A: This question is based on formation of perfect square and solving inequality notation.

Q: representing all lines passing thru (-1,1)

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Q: For the given p-series, identify p and determine whether the series converges. 4/3 k=1 p = Therefore...

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Q: Determine C when x=y=0 (xy + x)dæ = (x²y + æ² + y³ + 1)dy

A: Given that xy+xdx=x2y2+y2+x2+1dySolution :xy+xdx=x2y2+y2+x2+1dyxy+1dx=x2y2+1+y2+1dyxy+1dx=y2+1x2+1dy...

Q: The expression ả o (b × č) represents O a scalar O a vector O a line something that does not make se...

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Q: EXERCISE 2.3.1 Find D (-13). EXERCISE 2.3.2 Find D (8x). EXERCISE 2.3.3 Find D (x"). EXERCISE 2.3.4 ...

A: Topic = Derivative

Q: Find y''of 4cos(x/2)+e^-2x

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Q: 1. y+/x +y = x at ( 3, 1)

A: Part 21,Given,            y+x+y=x , 3,1To find : The equation of the tangent line and normal line.

Q: 2. Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 12 in...

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Q: 1. If f(x) = x² + 4x – 5 and g(x) = x – 1, then lim f(x) equals x→1 g(x) с. -1/6 а. -6 b. 6 d. 1/6

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Q: The differential equation 3y(x² –1)dx+(x² +8y– 3x}dy = 0; is exact because ƏM ƏN dy Əx

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Q: The expression ā o (b o č) represents O a scalar something that does not make sense O a vector O a l...

A: I am attaching image so that you understand each and every step.