University:
California State University, Northridge
Course:
MATH 255A | Calculus for the Life Sciences I
Academic year:

2024
Views:

282

Pages:

6
Author:

Lindsay Fuentes

MATH 255 A HOMEWORK- SECTION 2.1 1 #4. Average Rate of Chanye f(x) = -2x²+x+Y ou [1,4] (10)-(la) (-2.4²+4+4)-(2-1²+1+4) a- 4-1 #10. Approximate the rust. rate of chaye. 30+3-9. 3 = f(x) = -2x²+x+y at xay fc4th)-f(4) ho f'(4)= lim f(4th)-f(4) b b 4th 0.01 4.01 -15.02 0.01 3.99 -14.98 0.001 4.001 0.001 15.002 3.999 - 14.998 0.0001 4.0001 -15.0002 0.0011 3.9999 -14.9998 #28. Estimate the tangent by evaluating Secant slopeد y = sin 2 Si a=1 Sin (ath)-si- y-yo = m (x-xo) 1th 0.01 1.01 -0.0123 -0.01 0.99 0-0123 0.001 1.001 -0.0012 -0.001 0.999 0.0012 0.0001 1.0001 0.0001 -0.0001 0.9949 0.0001 Estimate f'(4)~-15 b yo = fla) = Sth=1 2 Estimate f'(a)~0 m = fía) y = 1 (hoviz.lize) Taugant line: = Xo = a = 1 A fy y=1 Tonynt line: y=1. 0 2 X #38. M Determine the sangent line by evaluatiry f'ca) algioraically. y=x² 2 at y-yo = m a = -1 (x-xo); xo = a =-1 yo-fla)=1 m = f'(a) = f(-1) 2 f'(-1) = h(-1th) -(-1)² = 470 = lem 1-2h th² -1 = -2th 2 h70 = -2. Tangent line: g-1=-2(x+1) y=1-2x-2 y=-2x-1 2 y=x -2x-1 MATH 255A HOMEWORK - SECTION 2.2 #14. Approximate the limit using a table: X3-8 lim g(x); g(x)= x²+2x+4 2- 1.0 1.5 1.9 1.99 1.999 1.9999 y -1 -0.5-0.1 -0.01 -0.001 -0.0001 J-Values appea to approach Estimate: lim g(x) = 0. x-2- #21 Determine the limits lim Vx+2-2 lim (√x+2-2) (√x+2+2) X72 lom X-2 (x+2)-4 Xx2 (x-2)x+2+2) lim x-2 2(1-2) (2+2) = 2(x-2)(x+2) ㅗ 2+2 X→2 √x+2 2 +2 √x+2 +2 x=2 す = = = #24. limi X4 (メー4) ((x-4) samme a 2 = bin 1x-412 1メー41 1x-4/2) bon 1x-41 x4 1x-411 = 0. 1x=4 = MATH 2557 7 HOMEWORK - SECTION 2.3 Determine the limits. #4: lim f(x) xa- bon blx), bin 400) x-> ax if they exist. 2 a=0 f(x)==씨 (x≠0) lim f(x) = low 181=0 x→0- x→0- Com f(x) = lom 1x1 =0 X-70+ lom Rix) = 0 since both of the limits. abre exist and are -0. #10. Find the limit! lon 1-2 (-2) (2) +70 +(4+2) +(4+2) 4-62-4 (14-212) = 047 - = the +70 / √2+2 = 1412 2+2 4-

Math 255A Homework Solution

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