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Material Type: Assignment; Professor: Kim; Class: Calculus I; Subject: Mathematics (MS); University: Jacksonville State University; Term: Unknown 1989;
Typology: Assignments
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Type a math expression. Use the expression palette to write more complex expressions. Right clicking on the expression displays a menu of operations Example1. How do we evaluate 2 C^3 ,^3 (^2) , p, 7 , sin(p ) , ln ( e )? >^2 C^3 5 > 3 2 : > evalf^ (^ p^ ) 3 . > sqrt ( 7 ) 7 > evalf^ (^ %^ ) 2 . > sin^ (p^ )
Example2. Solve the equation x 3 C x 2 K 7 x K 3 = 0. > (^) solve ( x^3 C x^2 K 7 x K 3 = 0 , x ) K 3 , 1 C 2 , 1 K 2 1 > evalf^ (^ %^ ) K 3., 2.414213562, K. Example3. Define a function f^ ( x^ )^ =^ x 2 K 5 x C (^3). (a) Evaluate f^ (^2 )^ and^ f^ ( x^ C^ h^ ). (b) Find the different quotient and simplify : f ( x C h )K f ( x ) h (c) Find the derivative of f(x) by evaluating the limit lim h / 0 f ( x C h ) K f ( x ) h
(d) Use the maple command diff or the operator d dx in the Expression pallete to differentiate f^ ( x^ )^. > (^) f := x / x^2 K 5 x C 3
Step 1. Define the function f^ ( x^ )^. > (^) f := x / x 6
( 2000 K x ) 2 C 600 2 4 f := x /
x C
( 2000 K x ) 2 C 360000 Recall the process of finding the global maximum or minimum value of a function. All we do is to compare the evaluations at critical points and end points. Step 2. Find the derivative of f^ ( x^ )^. > Df^ :=^ diff^ (^ f^ (^ x^ ),^ x^ ) Df :=
K 4000 C 2 x 4360000 K 4000 x C x 2 Step 3. Solve the equation Df^ =^ 0.^ Solutions of this equations are the critical points. > CP^ :=^ solve^ (^ Df ,^ x^ )
> evalf ( % ) 1
Step 4. Compare the values at the end points and the critical points. > f^ (^0 ) 50 109 > evalf ( % ) 5
> f^ (^200 ) 100 3
> evalf ( % ) 5
> f^ ( CP^ )
> Problem 2 (Due on Friday Nov. 10) Use Maple to solve the following optimization problem. Turn in a hard copy of your worksheet. A powerhouse is located on one bank of a straight river that is 150 feet wide. A factory is situated on the opposite bank of the river, 400 feet downstream from the point P directly opposite the powerhouse. What is the most economical path for a cable connecting the powerhouse to the factory if it costs 5 dollars per foot to lay the cable under water and 3 dollars per foot on land?
