maths work

1. fj What value of the constant c will make the following limit exist?

[( 2X + [x I) ]M~ x (x2 + C - 2)

following statements are true and give an explanation to justify your answer.

1

-6 -5 -4 -3 -2 -1 o 1 2 3 4 5 6

-1

(a). limx-->_2 f(x) = 1 (b).f( -2) = f(2)

-( \

(c). y = 3 is a horizontal asymptote of [,

(d).f'(l) = 4

(e). [is not differentiable at three values ofx.

(f). limX-.l [(x) = [(1)

(g). f' (-3) + f' (2.5) = 0

3. 4••• ~Find :~ for the following functions. Simplify your solution if possible.

(a). y = 41n(x2 - 3x + 4) (b). y = xtan(x)

(c). y = e21n(X)

4. ~ One bicyclist is 4 miles east of an intersection and is traveling toward the intersection at a rate of9 mph. At the same time, a second bicyclist is 3 miles south of the intersection and is traveling away from the intersection at a rate of 10 mph. Is the distance between the two bicyclists increasing, or is it decreasing? At what rate is the distance changing?

5..~ -' -~ Finding an equation of the line tangent to the following curves at the given point.

(a). y = 4x5 + cos x; X = 0

(b). xy +.JXY = 6; (x,y) = (1,4)