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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]
Write one or two paragraphs comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why.
A pilot, attempting to fly from Middletown to Westburg, a distance of 200 miles, notices after flying 180 miles that West burg is still 35 miles away because the heading was off by a few degrees.
Determine whether or not the argument below is valid. Transcribe it into symbolic notation and if it is valid, provide a derivation of the conclusion from the premises using only primitive rules of inference.
Find the point on the graph of the given function at which the slope of the tangent line is the given slope.
A central angle of a circle of radius 30cm intercepts an arc of 6cm the central angle in terms of degrees is? The reference angle of 3.22 rev?
Given the vector field F=3yi + (5-2x)j + ((z^2)-2)k find the surface integral of the normal component of curl F over the open hemispherical surface (x^2)+(y^2)+(z^2)=4 above the xy plane
The trigonometric expression to estimate the value
Find the equation of the tangent plane to the central conicoid x2 - 4y2 + 3z2 + 2 = 0 at the point (1,2,0). Find whether the plane 2x + 3y + 2z =3 touches the central conicoid 2x2 + 3y2 + z2 = 1 or not.
State the null and alternative hypotheses
Find the ninety-five percent confidence interval for the standard deviation of the ounces of coffee that a machine dispenses in 12-oiince cups. Suppose the variable & normally distributed.
Records at a high school indicate that each year for the past five years, 120 of the 1,500 students were absent on the first day of hunting season
A target heart rate T that is half a person's maximum heart rate is given by T=110 - 1/2A where A is a person's age.
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