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1. Find the limits. Show your work. a. lim Vx -5-1 x -+ 6 X - 6 U b. lim x - 8 4x+1 1 C. x+5 lim 8 X - 3 X-32. Find the equation of the tangent line at the specified points a. g x)=5x -2x+1 1,4 b. f x= x-1 at (1,0) 3x+2\f4. Use related rates to find the solution: a. The radius of a circle is increasing at a rate of 5 cm per minute. Find the rate of change of the area when r = 30 centimeters.5. Find the Absolute Extrema of the function on the closed interval. f (x) = - x2 [-5,5] x -+4 6. Find the following for the function, fx =x*-6x +4. Label the extrema as a maximum or minimum and write both the extrema and inflection points as (x,y). a. Increasing: b. Decreasing: C. Extrema: d. Concave up: e. Concave down: f. Points of inflection: 7. Find the differential to compare dy and delta y for y=x*+8 whenx=-1AAx=dx=0.018. Evaluate Indefinite Integrals: X+6 a. dx VX b. [3x5 -2x+ x3 dx C. cosx -8 sinx dx 9. Find the particular solution to the differential equation that satisfies the initial condition. a. g x = sin (x )+2 x given:g (0)=0Ag(0)=4 10. Find the area of the region bounded by the graphs of the equations. a. y=1+\\ xy=0, x=0, Ax=811. Given that J f(x)dx=4AS f(x)dx=-8 find: a. Sf ( x) dx 5 5 b. [ - 3f ( x) dx 3 c . Sf ( x lax 12. Use the second fundamental theorem sinx a. Find F'(x) given F(x)= S 2vt dt 0 b. Find F'(x) given F(x)= ] Vt2-1 dt 13. Using u-substitution X a. J dx 1+ x4 b. [(9+3 x) (3) dx C. 1 dx 1 V4x+514. Find the derivative of the function: a. fx = In 5x(x-+1) b. fx=x Inx 15. Find derivative using implicit differentiation a. In xy +9 x=10 b. x'+In3y=1 16. Evaluate definite integrals a. 1+ Inx dx 17. Find the indefinite integral: J 9 - x Adx 18. Is the following strictly monotonic? Why or why not? Does it have an inverse? a. fx =x -27x-+243x 19. Find an equation of the tangent line to the graph of the function at the given point: f(x) = e- In(x) (1, 0) 20. Find the indefinite integral: J e* v7-e* dx 21. Find the relative min, max, and any point(s) of inflection for the function: f(x=(1+xle*