Question

Let f be the function defined by f(x) = 12 exp(x2 – 3x). The function exp(u) is another name for e". a) Find L(x) the linear approximation to f at 3. L(x) = help (formulas) b) Use the Linear Approximation for f(x) = 12 exp(x2 – 3x) at 3 to estimate f(3.08). f(3 + 0.08) help (decimals). c) Find the error in the linear approximation to the value of f(3 + 0.08) that we found in part b). The error is (Use a calculator to get a decimal value.) d) Find the percentage that results from approximating f(3 + 0.08) by the value in part b). The percentage error is %. (do not enter "%")

Answer 1

10:21 AM Thu 23 Apr %LLIU O < 5 TON OG f(x)= 12 ex²-3x Linearization of fall at aza is given by : 262)= f(Q) + f'(a) (2-a) a=3 f(3) = 12 69-9 - 12 f2= 12 822-3x f'(a) = (20**) - 12 evlsk (4C2_30)] = (zemk3x) (2x-3) for 223 f(3) = 12x3= 6 da 3 L689 = 12 + 36 (2-3) (a) L(99 = 364 - 96 cby L(3.08) = 36 (3-08) -96 = 14088

10:21 AM Thu 23 Apr ini 11% 0 + < U © 5 TODO of @ @ f&-08 - 12 2 6092–3 (308) =15035 errore (3608) - L13-08) | error =004729 (D) ys of books are not to DDY error% = 3.0804 4fo © = F (3= lots + (054)s 8=50 ¢ go L(S) = f($9) + f'fo) (s-se] F (s) = 1017.1088 f'(so) = 605 F(9) - l-l() + 6054) Go)2 = 190 LO = 190 + 6.5(8-50) L(s)= Goss-135

10:22 AM Thu 23 Apr il ni 11% 0 5 TON of ☺ ☺ +30 L'(S) = 6.5 = f'(50) 7 Ans of (a) And of (b) = f (80) f' (20) = \.) + (109) do fl(60) = 9074 (³ 462) = -40-18 is linearization of 280) at n=-5 L() = 66-5) + h'cs) (22+5) = -48-18 compairing: hes) = -4 h65) +5 56-5) = -18 h(s)=-18+20=2=) h (5)=2 u= uha) Urs) = -5(2) = 40 ul) = f(x) + 1 ha) u(-5) = a + -564) = 22 K(1) = -10 + 22(x+5) =) K() = 222 +100
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