Numerade

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Kumareshwaran Rathinasabapathy

Numerade educator

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(1 point) Find the $ x $-coordinate of the first point in the region $ x>0 $ where $ y=3 x $ intersects $ y=\tan x $. Give your answer to 6 significant figures.

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Ipsita Mandal

Numerade educator

Suppose that 201 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as the following figure: Find the dimensions of the corral with maximum area. x = ft. y = ft. Find the point P on the graph of the function y = ?x closest to the point (9, 0) The x coordinate of P is: A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $3 per square foot and the metal for the sides costs $8 per square foot. Find the dimensions that minimize cost if the box has a volume of 50 cubic feet. Length of base x = Height of side z = A boat on the the ocean is 9 km from the nearest point on a straight shoreline; that point is 10 km from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. If she walks at 5 km/h and rows at 5 km/h. How far will the point on shore be from the restaurant if she plans to minimize her total travel time? Distance from restaurant = km Find a positive number x such that the sum of 36x and 1/x is as small as possible. x = Does this problem require optimization over an open interval or a closed interval? A. closed B. open

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Ipsita Mandal

Numerade educator

Consider the function f(x) = x^3 / (3x^2 + 5). List the x values of inflection points of the function f. If there are no inflection points, enter 'NONE'. Consider the function f(x) = 5x + 7x^-1. For this function there are four important intervals: (-inf, A], [A, B), (B, C], and [C, inf) where A, and C are the critical values and the function is not defined at B. Find A and B and C For each of the following intervals, tell whether f(x) is increasing (type in INC) or decreasing (type in DEC). (-inf, A]: [A, B): (B, C]: [C, inf) Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD). (-inf, B): (B, inf):

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Ipsita Mandal

Numerade educator

Let f(x) = e^{-2x^2}. Then f(x) has a relative minimum at x = a relative maximum at x = and inflection points at x = and x = Write DNE if any of the above do not exist. Write the inflection points (if any) in numerical order, smallest first. You are given the following graph of the function f(x): Find the point where the second derivative changes sign from negative to positive? x=

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Ipsita Mandal

Numerade educator

Use L'Hôpital's Rule (possibly more than once) to evaluate the following limit lim x?? (6x³+9x²)/(4x³-8) = If the answer equals ? or -?, write INF or -INF in the blank. Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than once. lim x??/2 sin(x-?/2)/cos(x+?) = Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than once. lim x?1 (1-e^(x-1))/(e^x - e) = Use L'Hôpital's Rule (possibly more than once) to evaluate the following limit lim t?0 (3 sin(12t) ln(12t)) = If the answer equals ? or -?, write INF or -INF in the blank. Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than once. lim x?-? (10x + 2)/(6x - 6) =

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Ipsita Mandal

Numerade educator

Use Newton's Method to find the two solutions of e^x = 6x to six significant figures. x_left = x_right = Use Newton's Method with the function f(x) = x^2 - 2 and initial value x_0 = 2 to calculate x_1, x_2, x_3. x_1 = x_2 = x_3 =

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Ipsita Mandal

Numerade educator

Find the x-coordinate of the first point in the region x > 0 where y = 3x intersects y = tan x. Give your answer to 6 significant figures.

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ANSWERED

Ipsita Mandal

Numerade educator

Suppose that 201 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as the following figure: x y Find the dimensions of the corral with maximum area. x = ft. y = ft. Find the point P on the graph of the function y = ?x closest to the point (9, 0) The x coordinate of P is: . A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $3 per square foot and the metal for the sides costs $8 per square foot. Find the dimensions that minimize cost if the box has a volume of 50 cubic feet. Length of base x = Height of side z = A boat on the the ocean is 9 km from the nearest point on a straight shoreline; that point is 10 km from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. If she walks at 5 km/h and rows at 5 km/h. How far will the point on shore be from the restaurant if she plans to minimize her total travel time? Distance from restaurant = km Find a positive number x such that the sum of 36x and 1/x is as small as possible. x = Does this problem require optimization over an open interval or a closed interval? A. closed B. open

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ANSWERED

Ipsita Mandal

Numerade educator

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Jany b.