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Danish Khan

Danish K.

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Find two numbers whose difference is $ 100 $ and whose product is a minimum.

Find two numbers whose difference is $ 100 $ and whose product is a minimum.

Calculus: Early Transcendentals

Applications of Differentiation

Optimization Problems
Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, $ 3 ft $ wide, by cutting out a square from each other of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases. Find the volumes of several such boxes. Does it appear that there is a maximum value? If so, estimate it. (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols. (c) Write an expression for the volume. (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the volume as a function of one variable. (f) Finish solving the problem and compare the answer with your estimate in part (a).

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, $ 3 ft $ wide, by cutting out a square from each other of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases. Find the volumes of several such boxes. Does it appear that there is a maximum value? If so, estimate it. (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols. (c) Write an expression for the volume. (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the volume as a function of one variable. (f) Finish solving the problem and compare the answer with your estimate in part (a).

Calculus: Early Transcendentals

Applications of Differentiation

Optimization Problems
a. The radius of a circular juice blot on a piece of paper towel $t$ seconds after it was first seen is modelled by $r(t)=\frac{1+2 t}{1+t},$ where $r$ is measured in centimetres. Calculate i. the radius of the blot when it was first observed ii. the time at which the radius of the blot was $1.5 \mathrm{cm}$ iii. the rate of increase of the area of the blot when the radius was $1.5 \mathrm{cm}$ b. According to this model, will the radius of the blot ever reach $2 \mathrm{cm} ?$ Explain your answer.

a. The radius of a circular juice blot on a piece of paper towel $t$ seconds after it was first seen is modelled by $r(t)=\frac{1+2 t}{1+t},$ where $r$ is measured in centimetres. Calculate i. the radius of the blot when it was first observed ii. the time at which the radius of the blot was $1.5 \mathrm{cm}$ iii. the rate of increase of the area of the blot when the radius was $1.5 \mathrm{cm}$ b. According to this model, will the radius of the blot ever reach $2 \mathrm{cm} ?$ Explain your answer.

Nelson Calculus and Vectors

The Elasticity of Demand

The Quotient Rule
$m=9.00 \mathrm{~kg}$

$m=9.00 \mathrm{~kg}$

Applied Physics

Force

Gravity and Weight

Questions asked

ANSWERED

Vincenzo Zaccaro verified

Numerade educator

Question 12 Consider the function f(x) = 2^(x^2) cos x. Using a linear approximation of this function centered at the point x = 1, estimate f(x) at x = 2. (round to one decimal place)

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ANSWERED

Eduard Sanchez verified

Numerade educator

Question 11 1 pts Find the critical numbers of the following function f(x) = 2x^5 + 9x^4 + 8x^3. How many critical numbers does this function have? 4 1 3 2

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ANSWERED

Vincenzo Zaccaro verified

Numerade educator

Question 9 1 pts Consider the integral int_{1}^{4} ln (x+2) dx. Find the approximate value using the right endpoint rule with 10 rectangles. Round your answer as a decimal correct to 5 decimal places.

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ANSWERED

Penny Riley verified

Numerade educator

Question 8 1 pts Evaluate ??? e?²? x³ dx. Round your answer as a decimal correct to 5 decimal places.

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ANSWERED

Supratim Pal verified

Numerade educator

Question 7 1 pts If x^2 sec(y^2) = ln(sin(sqrt(x))), find y' at (1,2). Answer this in decimal form, rounded to four decimal places.

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ANSWERED

Eduard Sanchez verified

Numerade educator

Question 6 1 pts Simplify the expression cos(tan^{-1}(5x^3)). Choose one correct answer from given answers. ? 1 / sqrt(25x^6 + 1) ? 5x^3 / sqrt(25x^6 + 1) ? 1 / sqrt(25x^6 - 1) ? 1 / sqrt(-25x^6 + 1)

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ANSWERED

Supratim Pal verified

Numerade educator

Evaluate the following limit: lim x->0 2x / (1 - e^-x). What is the value of this limit?

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ANSWERED

Penny Riley verified

Numerade educator

Question 4 Consider the function f(x) = e^(x^3/3 + 5x^2/2 + x - 3). How many local maxima/minima are there in the interval [-2, 2]? (e.g. if you get a local maximum/minimum at x=-1 and x=1, then your answer should be "2") 3 2 4 1

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ANSWERED

Nicole Smina verified

Numerade educator

Solve x^3 - 21x^2 + 147x - 343 = 0. State the solution rounded to one decimal place).

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ANSWERED

Supratim Pal verified

Numerade educator

For each of the following questions, clearly select the ONE correct answer. Which of the following functions is concave down on the interval (-1,0)? x cos(2x) -e^{x+4} 2x sin x e^{-x^3}

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