Review Test 1 Oct 25, 2024 PDF

(10125/24) SESSION = VIEW (PREREQUISITE FOR COURSEL * *...

(10125/24) SESSION = VIEW (PREREQUISITE FOR COURSEL * * &: WHAT KIND Of PROBLEMS WERE ON WORKSHEE AND HOMEWORK , AND In CLASS ?  (10125/24) SESSION = VIEW > - LIMITS AT I O - &: WHAT KIND Of PROBLEMS WERE ON WORKSHEE AND HOMEWORK , AND In CLASS ?  (10125/24) SESSION = VIEW ~ * LIMIT EXISTS ! * - ~ &: WHAT KIND Of PROBLEMS WERE ON WORKSHEE AND HOMEWORK , AND In CLASS ?  TRANSFORMATIONS FUNCTIONS (MODELS) LINEAR ON - Look POWER FUNCTION y = f(x) = x* LOG-LOG PLOT EXPONENTIAL FUNCTIONS - = f(x) = c bY SEMI-LOG PLOT ↑ ① · no ② logio y · GIVEN THE LINEAR FIT (RED) - to THE DATA (BLUE) WHAT , IS THE RELATIONSHIP BETWEEN & AND Y ? log GIVE YOUR ANSWER IN THE FOR y = f(x) ·  * its linf(x) , limi y & line to * Note : Lim X = 0 = O Know X X >0 - BASIC * - LIMITS ! FOR eine e * = - lim = 0 X > Is - * -> 0 * - - x etc. * FOR thi f(x) MAINLY WORRY ABOUT LIMITS WITH , X = c O INDETERMINANT FORMS J 5 ① FIND THE FOLLOWING LIMITS (i) line ii lime. ① FIND THE FOLLOWING LIMITS iii) him a (iv) him a (v) limit A = Wis line * RIVATIVES RATES Of CHANGE ! SLOPES ! f'(x) = lim f(x) = y = f(x) · Sx = h TAKE - * 0 To FIND f(x) & Find THE DERIVATIVES Of FUNCTIONS : POWER FOR RULE DERIVATIVES f(x) = x * f(x) = axa - 1 & SCALAR MULTIPLO & dX (a f(x) + bg(x)) AND ADDITION RULE adx b FOR DERATIVES = + a B PERIVATIVES OF KEY FUNCTIONS (ex) ex = A GIVEN ON EXAM. ⑨ FIND TE DERIVATIVES OF THE FOLLOWING FUNCTIONS : Ax (i) f(x) + By C D = - + 2 4 y0 - (ii) g(y) = (iii) R(s) =  * (iv) f(t) = a sint + be + E a , b , m POSITIVE CONSTANTS ()h(v) = rN)) - ) -K Positive Construts 2et sint e (vi) y(t) = + + ② FIND THE DERIVATIVE OF f(x) = (2x -4)(x + 5) (1) USING RULES OF DIFFERENTIATION. (ii) USING THE LIMIT DEFINITION Of The Derivative. ② FIND THE EQUATION FOR The TANGENT LINE OF f(x) = * At X = 2. ⑧ - & ⑨ WHAT ARE THE UNITS OF P(t) > ALSO - , APPROXIMATE P'(O) PC6 5). And P'(16). , ,