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Chapter 7: Q. 3 (page 639)

Let p(x)be a nonzero polynomial function. Evaluatelimx鈫�鈭�p(x+1)p(x).

Short Answer

Expert verified

If p(x)=鈭�k=0鈭�akxkthen the value oflimx鈫�鈭�p(x+1)p(x)is1.

Step by step solution

01

Step 1. Given information. 

The given expression that needs to Evaluate islimx鈫�鈭�p(x+1)p(x).

02

Step 2. polynomial function.

Consider a polynomial,

p(x)=a0x0+a1x1+a2x2+鈰�+anxnp(x)=鈭�k=0鈭�akxk

So the value of p(x+1)will be the following.

p(x+1)=鈭�k=0鈭�akx+1k

03

Step 3. Value of limx→∞p(x+1)p(x).

Determine the value of limx鈫�鈭�p(x+1)p(x).

limx鈫�鈭�p(x+1)p(x)=limx鈫�鈭�akx+1kakxk=limx鈫�鈭�x+1xk=limx鈫�鈭�1+1xk=1k+0=1

So the value oflimx鈫�鈭�p(x+1)p(x)is1.

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