WH2_M1151_SU23.pdf * *Homework Help - Q&A from Or x -> C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&... (5 BO H Men Custom Suits... OBAMASEX.. O BERTHS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car.. E WH2_M1151_SU23.pdf 2 / 6 100% + Problem 1: Secant and Tangent Lines of a Piecewise Function (36 points) A piecewise defined function g is given by the formula 8 ( x ) = - x+1 if x 54 4 V X - 7 if x > 4 A partial graph of this function is given below. In this problem, we will find secant and tangent lines to this function. 3 y = 8(x) 2 -2 -1 3 5 6 a) (2 points) On the graph above, draw the secant line of g(x) between x = 0 and x = 6. Label this line with a large S. 3 b) (2 points) Find the slope of the secant line you drew in Part (a). Slope: c) (3 points) Find an equation of the secant line you drew in Part (a).WH2_M1151_SU23.pdf * *Homework Help - Q&A from Or x -> C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... (b H Men Custom Suits... OBAMASEX.. O BERHR($ 20... b Big Dude USA - Bi... 20 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... E WH2_M1151_SU23.pdf 3 / 6 100% + c) (3 points) Find an equation of the secant line you drew in Part (a). Equation: d) (2 points) On the graph above, draw the line tangent to g(x) at x = 3. Label this line with a large T. Math 1151, Summer 2023 Written Homework 2 Page 3 of 6 2 e) (2 points) Evaluate g(4). 8 ( 4 ) = f) (4 points) Use the definition of continuity to verify that g(x) is continuous at x = 4. (Do not use the graph for this part. We want to verify that the graph is displayed correctly.) 3 8) (4 points) For x C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... (dj H Men Custom Suits... OBHBASES.. O BRAHMA($ 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... E WH2_M1151_SU23.pdf 3 / 6 - 100% + 8) (4 points) For x C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... (b H Men Custom Suits... O BRASEXE... O BRAHHER($ 20... b Big Dude USA - Bi... 30 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... E WH2_M1151_SU23.pdf 4 / 6 100% + i) (4 points) For x > 4, find a formula for ) SIMPLIFY your result. x - 4 g ( x ) - 8 (4 ) x - 4 i) (4 points) Evaluate lim 8(x) -8(4) x - 4 2 3 lim 8 ( x ) - 8 ( 4 ) 1 -+ 4+ X - 4 k) (2 points) Use your answers from above to determine if g (4) exists. Explain.WH2_M1151_SU23.pdf * *Homework Help - Q&A from Or x -> C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... (bj H Men Custom Suits... OBAMASEX.. O BERHR($ 20... b Big Dude USA - Bi... 20 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... E WH2_M1151_SU23.pdf 4 / 6 100% 8 (x) - 8(4) x - 4 j) (4 points) Evaluate lim 8(x) -8(4) x - 4 2 lim 8 ( x ) - 8 ( 4 ) x - 4 k) (2 points) Use your answers from above to determine if g'(4) exists. Explain. 3 I) (3 points) Find an equation for the line tangent to g(x) at x = 4, if this line exists. If this tangent line does not exist, explain why. Equation:WH2_M1151_SU23.pdf * *Homework Help - Q&A from Or x -> C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... d H Men Custom Suits... OBHBASEME.. O BERHR($ 20... b Big Dude USA - Bi... 30 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... E WH2_M1151_SU23.pdf 5 / 6 100% Problem 2: Temperature in a Microwave (24 points) Saul the college calculus student wants to reheat some pizza between study sessions. Saul puts the pizza in the microwave straight from the refrigerator. When the pizza has been heating up for t minutes, its temperature is given by r(t) = 2+5 + 37 where r(t) is measured in degrees Fahrenheit. We will use calculus to study how fast the pizza heats up. a) (2 points) What was the temperature of the pizza when Saul took it out of the refrigerator? (Include units.) 2 Temperature: b) (2 points) Saul wants the pizza to be 165. How long should he microwave the pizza to hit this temperature? (Include units.) 3 Time: c) (4 points) Find the average rate of change of the temperature of the pizza during the first two minutes. (Include units.) Average rate of change: d) (4 points) Find the average rate of change of the temperature of the pizza during the time interval [1, 3). (Include units.)WH2_M1151_SU23.pdf * *Homework Help - Q&A from Or x -> C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... (d H Men Custom Suits... O BEBASEDE... O RRHHRS 20... b Big Dude USA - Bi... 30 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... WH2_M1151_SU23.pdf 6 / 6 100% + d) (4 points) Find the average rate of change of the temperature of the pizza during the time interval [1, 3]. (Include units.) Average rate of change: 3 =4 - Math 1151, Summer 2023 Written Homework 2 Page 6 of 6 e) (4 points) Let An denote the average rate of change of the temperature during the time interval [3, 3 + h] if h > 0, and the average rate of change of the temperature during the time interval [3 + h, 3] if h C production-gradescope-uploads.s3-us-west-2.amazonaws.com/uploads/pdf_attachment/file/109256666/WH2_M1151_SU23.pdf?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Am... (d H Men Custom Suits... O BRASEX.. 0 9RXHR18 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... WH2_M1151_SU23.pdf 6 / 6 - 100% + Ah = f) (3 points) Evaluate the limit lim Ah. (Include units). 3 lim Ah = g) (3 points) Explain what the value found in the previous part means in the context of the problem. (Don't forget units.) =4 - (Your answer should specifically mention Saul's pizza.) h) (2 points) Saul's plate might crack if its temperature ever changes at a rate faster than 50/ min. Is the bowl in danger of cracking at time t = 3? Explain your