Question

13. Consider

f(x)=sqrt x-2

a) Using any of the three limit formulas to find f ′ ( a ), what is the slope of the tangent line to f ( x )at x = 18? (6 points execution, 2 points notation)

b) Find the equation of the tangent line at x = 18

14. State the derivative.

a) d/ d x [ x ^n ]

b) d /d x [ cos ⁡ x ]

c) d /d x [ csc ⁡ x ]

d) d/ d x [ cosh ⁡ x ]

e) d/ d x [ ln ⁡ x ]

f) d/ d x [ a x ]

g) d /d x [ sin ^− 1 ⁡ x ]

h) d/dx [ tan^ − 1 ⁡ x ]

15.Differentiate. Do not simplify.

f(x)=-4x^5+3/2x^3+x^⅔+10+7x^-2

16.Differentiate. Do not simplify.

g(x)=x^3secx

17. Differentiate. Do not simplify.

y=5sin (5x^2)+e^3x

18.Differentiate. Do not simplify.

k(x)= ln(tan x/3x)

19. Differentiate. Do not simplify.

n(t)=5t3^t cot t

20.Find the equation of the tangent line to the curve at the point ( 0 , 2 ).

              g(x)=e^x+1/x+1

21.Use implicit differentiation to find the slope of the tangent line at

( π , π/ 2 ).

xsiny+2x-2y

Answer 1