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Evaluate the following limits using l'hopital's Rule1) lim x->2 x^2-4x+4 / sin^2(πx)2) lim x->0^+ x^2x3)lim x->0 (x+cosx)^1/x4)lim x->π/2^- (tanx-secx)solution:1)1/π^22)13)e4)0Mean Value Theorem
a. Determine whether the mean value Theorem applies to the following functions on the given interval [a,b]
b. If, so find or approximate the point(s) that are guaranteed to exist by the mean value theorem.
c. Make a sketch of the function and the line that passes through (a,f(a)) and (b,f(b)). Mark the points P (if they exist) at which the slope of the function equals the slope of the secant line. Then sketch the tangent line at P.1)f(x)=arcsinx; [0,1/2]Only parts a & b.solution:a) yesb)c=√(1-9/πˆ2)2)f(x)=x/(x+2); [-1,2]
There are three consecutive even integers. If twice the first integer added to the third is 268,252, what are all three integers?
A Pyramid is 785 ft high (due to erosion, its current height is slightly less) and has a square base of side 3140 ft. Find the work needed to build the pyramid if the density of the stone is estimated at 180 lb/ft^3.
Find the equation of the plane passing through (3,4,-1) and parallel to the vectors A=2i+j+k and B=i-3k.
To order meat to be grinded at the meat factory cost 1/10 of the meat as the fee. If you need 2 pounds of meat, how much meat will the meat factory have to grind?
The height of a projectile fired vertically into the air (neglecting air resistance) at an initial velocity of 112 feet per second is a function of the time and is given by the equation f(x) = 112x - 16x2, where x represents the time. Find the hig..
Probability. Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma
A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees.
Find the second derivative
Find the slope of the line shown and interpret the slope as a rate of change given the following information. I am supposed to present this in business terms using Exxon Mobile as the example and using the mathematical concept of slope and rate of..
An open box is to be made from a square piece of sheet metal, 20 inches on a side, by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.
Finding the difference of the side lengths of a triangle - Find the smallest possible value of BC - AB?
Hits on a personal web site occur quite infrequently. They occur randomly and independently with an average of five per week.
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