2 use the piecewise defined function ( ) to arower the questions which follow 1 Evaluate the following limits using the algebraic X 45 properties of limits : Itlint you may Use in this problem at 52+5 x- 60 = 5(x-3) (x +4)- 2 x - 8 * 25 6x2 + 12x - 40 6 ( x - 2) ( *14 ) - - Consider the piecewise defined function !(x ) a ) what is lim fx ? and find the value of a which makes the function a lim 3x3 + 4x2 2x +7 Continuous o) lim 5x2+5x-60 x-73 6ex2+ 12x - 40 b ) what is lim , feet ? G) lim 5x 15x-60 4 using the formal limit definition of the derivative 6x2 + 12x - 40 c ) what is a f (s ) ? find the derivatives of flo = x2 + 7x. A maxinium of 3 points will be awarded if derivative techniques are used instead of the limit definition . d lim * - 7 2 + 5x2 + 5 x- 40 6x2 + 12X - 40 d ) Explain whether the following limit Exists or does hot exist lim fox) x- 75 e) lim 5x2+5 x- 60 6x 2+ 12 x - 40 ) Explain whether f ( x ) is continuous or not continuous at X = 5 @ Let f ( x ) = 2 x 3 - 4 x 2 + 5 x + 6 /3 141 1 (I one of the United Petroleums offshore drilling 5) Using derivative techniques ( power rule ( Sum rule ) (product Rule ) operations has developed a leak . The leak is causing a the. calculate the following derivatives ( you do not need to simplify ) ( a ) what is the point on the graph of ye ful when xel ? Circular oil spill . Whose radius ( in feet ) + hours after the leak began is given by the function r(t ) = vi + 2t a ) [ (x 3 - 3x2 + 13x - 7 ) The company estimates that it's clean up cost will be $7,500 per square foot affected . Use that area of a circle is given by Alt ) = Tix 2 to find : 6) Find y' given y= ((x 2 +7x- 10)( 243 - 4x3 + 3) b ) what is the derivative of fox) ? (9 ) The price to clean up the Spill after 10 hours ( ) let f h ) = 5x2 - x +7 find fix ) . "( ) what is the slope of the tangent line which passes through the point on the graph of y = f ( ) when x = 1 ? d ) If y = 61x - yo what is toy ? b ) The rate at which the price to clean up the spill is changing after 10 hours . I) what is an equation for the tangent line through the ) Given fox) = V- x2 +4x +9 what is ife ? point on the graph of 4 = fix). when * = 1