Calculating limits The following limits are the derivatives of a composite function g at a point a. a. Find a possible function g and number a. b. Use the Chain Rule to find each limit. Verify your answer by using a calculator limx→04+sin⁡x−2x

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Calculating limits The following limits are the derivatives of a composite function g at a point a.  a. Find a possible function g and number a.  b. Use the Chain Rule to find each limit. Verify your answer by using a calculator  limx→04+sin⁡x−2x

2k1enyvp · Accepted Answer

limx→04+sin⁡x−2xa. It can be written as,limx→04+sin⁡x−2x=limx→04+sin⁡x−4−sin⁡0x−0Now comparing with limx→ag(x)−g(a)x−a, we getg(x)=4+sin⁡x and a=0b. Differentiating g(x)=4+sin⁡x with respect to x, we getg′(x)=124+sin⁡x⋅d(4+sin⁡x)dx=124sin⁡x⋅(0+cos⁡x)=cos⁡x24+sin⁡xTherefore,limx→04+sin⁡x−2x=limx→04+sin⁡x−4+sin⁡0x−0=g′(0)=cos⁡0{24+sin⁡0}=14By using calculator, we getlimx→04+sin⁡x−2x=14

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Calculating limits The following limits are the derivatives of a composite funct

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