3 C. lim x - tanx sinx 2 ) d. lim sin 3x 1 0 3x + 6x2. Evaluate the following limits. 3 a. lim Sin' 2x x-0 Sin' 5x 3 b. lim Cos 2x - cos x x-0 coSx - 1c. lim 4 tan.x Note: You must derive the limit by the use of appropriate identity I-D X substitution of tan x in terms of sin x and cos x as your first step. 2 d, lim cos.x3. Differentiate the following trigonometric functions. Simplify 1where possible. This includes using double angle identities 1where possible to shorten the expression of the final solution. a. fix} = 1'; out; + 5x (9 lo. fix} = oosix2 - 2}: (9 o. y = sinllfJUr} d3 . 4. Find f} for y = cosTx. 5. Use implicit differentiation to find the derivative of the following relation, with respect to x. Simplify the derivative as much as possible. sinx + c0511: = 2.x}: 2 7. Find any possible inflection points for the function f(x) = sinx on the interval (0, 2x).sin 2.1 max 3. Find the equation of the line tangent to the curve fix} = at the paint {1 52 } 41