Math 180 -Assignment #1 Due: 10:00a, Saturday, January 23, 2021 ************************************************************************** *Complete solutions using proper notation will be required to receive full credit. *Please clearly identify your final answers. Circle your final answers where appropriate. *Please put your problems in numerical order before submitting them as a single PDF or Word Document via Blackboard. *Do NOT wait until the last minute. Late submissions will receive severe reductions. *Each problem will be graded on a 10-point scale. The total will be scaled to 100 points. ***************************************************************************** 5 #1.) Prove lim  − x + 7  = −8 using the  −  definition. x→6  2  #2.) Evaluate ( lim 4 x3 − 6 x2 + 7 x →−2 ) by demonstrating the properties.  3,   1 x + 1, #3.) Given f ( x ) =  2  5,   x 2 − 2, a.) lim + f ( x ) x →−4 b.) lim f ( x ) x → 0− c.) lim f ( x ) x → 0+ x  −4 − 4 x  0 x=0 , Evaluate the following limits. x0 You might find a graph helpful but I am looking for an analytical approach using the piecewise-defined function given above. #4.) Evaluate lim x →−1 #5.) Evaluate lim x→9 x+5 −2 . x +1 3x 2 − 4 . x−6 1 1 − x+3 5. #6.) Evaluate lim x→2 x − 2 #7.) Evaluate 3x −10 lim + . x − 4 x →4 Hint: 3x −10 2 = 3+ x−4 x−4 #8.) Given f ( x ) = 2 x2 − 3x , Find lim x → 0 f ( x + x ) − f ( x ) . x