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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]
on three consecutive passes, a football team gains 9 yards, loses 16 yards, and gains 30 yards. What number represents the total net yardage?
Find the mass and center of mass of a wire in the shape of a helix x=t,y=cos(t), z=sin(t), 0
The length of a rectangular room is 3 feet longer than twice the width. If the room's perimeter is 174 feet, find the length of the room.
The average of two numbers, a and b, is given. The average is 75 one number is 91, what is the other number? Please show all work.
A surveyor standing 66 meters from the base of a building measures the angle to the top of the building and finds it to be 36°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 45°. How tall i..
the life of battery distributed with mean of 120 days and standard deviation of 5 days. What is the minimum number of days for the life time of randomly selected battery in order it can be top 10% of life time.
Find the indicated probability.Find the indicated probability.
ate the expression. where necessary, enter your answer as a fraction using the slash (/)as the fraction bar 6/11^2.
A catering service has been asked to provide a lunch buffet the next day for 40 people at a set price of $10.50 per person; no function has been booked for the next two days.
What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)
Ace manufacturing has determined that the Cost of Labor for producing x transmissions is: 0.3x(squared) + 400x+550 dollars. While the Cost of Materials is: 0.1x(squared) + 50x+800 dollars Write a polynomial that represents the total cost of Materi..
Write a compound inequality that expresses the range expect ot spend.
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