lim x→3 (x3 − 13x2 + 51x − 63) / (x3 − 4x2 − 3x + 18) = a / 5 Find the value of a. (It is supposue to be -4. Why?)

lim x→3 (x3 − 13x2 + 51x − 63) / (x3 − 4x2 − 3x + 18) = a / 5 Find the value of a. (It is supposue to be -4. Why?)

If f(x) = sinx, evaluate f(2+h)-f(2)/h to two decimal places as h approaches 0. Help?!

Evaluate the following limit: sinx/tanx as x approaches 0. Help?!

Prove sec2x-1=sec2xsin2x, justify significant steps. (state identities used)

Evaluate the following limit: lim of sin(4theta)/(5theta) as theta approaches 0. Help!?

Evaluate the following limit: Limit of xcotx as x approaches 0.

Prove sinx/1+cosx + 1+cosx/sinx = 2 cscx, Justify significant steps. Help!?

Find the slope of the tangent to the curve f(x) = x2-2x-1 at the point (3,2)

Find the slope of the curve 8x2+y2-2x+4y=270 at the point (-5,6). Round the answer to the nearest thousandth. Help!?

At what point is the tangent to the curve defined by the function f(x) = 4x2-x+5 parallel to the line y-15x=1? Help!

Determine the slope of the normal line to the curve y = x+1/x at the point (2,5/2). Round to the nearest hundredth.

What is the derivative of 2xy-17=-3x2? Is it -y/x-3?

Find the equation of the tangent line to the curve 3xy = x3+y3, at the point (2/3,4/3). HELP!?

Differentiate y = (2x+5)^3(6x-1)^5. Express your answer in factored form.

Find the slope of the tangent to y = 3x^2-6x at x =2 by first determining the derivative of the function from first principles.

Differentiate 2xy-17=-3x2 to find the slope at point (2,5). help?!

Find the point on the curve y = sqrt 2x-1 where the tangent line is parallel to the line x-3y=16. Help!?

If 2y2-xy-x2 = 0, find dy/dx. And, determine the slope of the tangent at x =1.

Find dy/dx if 2x5+x4y+y5 = 36

You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by v(t)=−5t4+41t3−147t2+170t. At noon you were 145 miles from home. At 3:00 you...