Question

Sa. sec(ax) •dx Va? - tan(ax) 5b. 35 (Ine)? dx 25 + (inverse trig functions) 7. The split method 6. Extended substitution 2x + 7 ſsin 2x \sin x – 3 dx •dx r? +6x +10 (5 points) 3x + 7 y 8. (5 points) Find the equation of a line that is tangent to a cure 2x+3 at (1,2). Leave the answer in the slope and y-intercept form as y = mx+b. No need to graph any picture at all. 9. (5 points) A 10 feet long ladder that was leaning against the wall as shown below. A guy was pushing the lower end of the ladder toward the wall and his action made the top end of the ladder moving up against the wall at the rate of 4 feet per second. How fast was the lower end of the ladder moving toward the wall when the lower end was 8 feet away from the wall? and at the moment what was the rate of the area of the right triangle that was formed by the ladder with the wall and the ground was decreasing? (NOTE for full credit: label all sides as A= the wall, B = the ground and C = the ladder) Lace

Answer 1

5.(a) da Pubstitute Seilan) vătan (2x) dz 21- is tan Case) = 2 -> a see (as) da=dz => See (ax) dx = dz Jazz ä Sin (2) + c sin' I tan lare) + c 2 -10 where C is arbitrary constant 5.(6) 35 da 25+ (lueta? 35 da 25+(70)? 35 = 35 shot ( 72 ) Scena ay trü (ſ)+c = new tamil (ta)+c e tail () + ( 49 25 z 49 tx (3) + x2 49 AC

(6) da 2 Sin 22 ſsin a-3 S sinx Sin & Cosa √ Sina-3 da ( (3+2)2.22 56323 32 +24) dz - 4{3 (2+dz + Sz" dz} substitute, Sina- 3 = 2 = Cosa da = 2z dz also, Sina = 3+2² = 2 .22 da 3 2² { 3 + } te 3 3 = 423 t z + C 3/2 + 5/2 = 4 (Sin 2 - 3) 2/2 (sin x-3)" + c

(7) da 2x+7 + 6x +10 2246 a+60+10 dat ( sa Gatio dat slechts to 17 la +6x+10) +62+10 = enla+ba+10l + tan (2+3) + (8) given, y = de la 3x+7 2x+3 (22+3). 3 - ( 3x+7). 2 (2x+3)2 dy an 1 sat T (2a+33 da (2+3)? (1,2)=- :: equation of tangent, y - 2 dy leviz xal 가 > y = -(4-1) +2 =) y = - š x+y