1. Find the equation of a line passing through point (5, -2) with slope ¾. (State your answer in slope-int. form)

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1 INTRO TO CALCULUS REVIEW FINAL EXAM NAME: DATE: A. Equations of Lines (Review Chapter) y = m + b (Slope-Intercept Form) A + By = C (Stanar Form) y y = m( ) (Point-Slope Form). Fin the equation of a line passing through point (5, -) with slope ¾. (State your answer in slope-int. form). Fin the equation of the line passing through the points (-, ) an (, -4). (State your answer in stanar form). Fin an equation for a line parallel an an equation for a line perpenicular to the line 4 y = an passing through the point (, 4). Write your answers in stanar form. B. Solving Equations (Review Chapter).) Quaratics try to solve by factoring or quaratic formula..) Rational Epressions multiply each term by the LCD to einate fractions..) Raical Equations Isolate the raical first, then uno root by squaring both sies ( ), cubing both sies ( ), etc. Solve each equation for all real values of = = = = + ( + )( ) = 7 C. Domain an Range (Review Chapter) Domain the set of -values for a relation or function. Range the set of y -values for a relation or function. Determine the omain an range for each. 9. = 0. =. + = + +

2 D. Limits (Chapter ) To evaluate its try:.) Direct Substitution.) Test values that approach..) Try to factor an cancel any common factors E. The Derivative (Chapter ).) Definition of the Derivative f '( ) = Δ 0 f ( + Δ) Δ.) Power Rule: f() = a n f () = na n-.) Prouct Rule: f() = g() h() f () = g() h () + h() g () 4.) Quotient Rule: f() = g( ) h( ) f () = h( ) g' ( ) g( ) h' ( ) [ h( ) ] 5.) (sin ) = cos 6.) (cos ) = sin *In orer for a function to have a erivative on any open interval (a, b), then the function must be continuous on (a, b) an not have any sharp points on (a, b). E: Function is not ifferentiable at = (Sharp point) Function is not ifferentiable at = 0 (Not continuous.)

3 8. Fin f () using the efinition of the erivative. f() = + For #9 0, fin the erivative using any metho. 9. = 0. =. + =. =. f() = ( )( + + ) 4. f() = cos( ) 5. f() = sin + sin 6. f() = cos 7. + y = y + y = 6 9. y = cos (4) 0. f () =. Fin f () if f() = + sin. Fin the slope of the line tangent to the curve f() = ( )( ) at (0, ).. Fin the equation of the line tangent to the curve = at (, 4)

4 4. Fin the point(s) where the graph of f() = + has a tangent line with slope = 0. F. Etrema an Critical Values (Chapter ) First Derivative Test: If f () > 0, the function is increasing. If f () < 0, the function is ecreasing. If f () = 0, the function is constant. Secon Derivative Test: : If f () > 0, the function is concave up. If f () < 0, the function is concave own. If f () = 0, the function is linear (no concavity). Asymptotes: a.) Vertical Asymptotes Set enominator = 0 an solve for. coefficient of highest in num. b.) Horizontal Asymptotes Fin highest power of. HA = y = coefficient of highest in en. c.) Oblique (Slant) Asymptotes) Long ivision an rop the remainer. (Only occurs if the egree of the numerator is eactly one larger than the egree of the enominator.) 5. Determine the intervals where f() = ¼ is increasing. 6. Fin all mas, mins, an inflection points of f() = Determine the intervals where f() = is concave own. 8. Fin all asymptotes. a.) = b.) = Fin the ifferential, y. a.) y = b.) y = sin +

5 G. Integration (Chapter 4) Rules for Integration: n+ n. = + C n + n. k = k n. sin = cos + C 4. cos = sin + C 5. = F( b) F( a) b a Problems. Evaluate each integral ( + ) sin cos 44. ( 4 ) 45. ( + ) 0 cos 46. sin 47. sin

6 H. Logarithmic an Eponential Functions (Chapter 5) Properties of Logarithms ln() = 0 log a = 0 lnab = lna + lnb logab = loga + logb ln a = lna lnb b ln(a n ) = nlna loga n = nloga log a = loga logb b Derivative of ln: (ln ) = has to be greater than 0 (lnu) = u u must be greater than 0 u Integral of ln: = ln + c u u = u = lnu + c u Derivative of e (e ) = e (eu ) = e u u Integrative e e = e + c e u u = e u + c Derivative for base other than e (a ) = (lna)a (log ) = a (ln a) u (au ) = (lna)a u (log u) = u a (ln a)u Integral of base other than e a = a lna + c a u u = au lna + c

7 Fin the erivative. f () = ln( + ). f () = ln( +) + ln( 4). f () = ln ( + 4) ( ) 4. f () = ln 5. f () = e 4 6. f () = e 7. f () = 5 8. f () = f () = log ( ) 0. f () = log 4 (6 + ). f () = log 4 +. f () = 0 Fin the Integral. e 5 (6) sin + cos

8 ( +.5) 7. e + ( +) ( )