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Let p(x)be a nonzero polynomial function. Evaluatelimxp(x+1)p(x).

Short Answer

Expert verified

If p(x)=k=0akxkthen the value oflimxp(x+1)p(x)is1.

Step by step solution

01

Step 1. Given information. 

The given expression that needs to Evaluate islimxp(x+1)p(x).

02

Step 2. polynomial function.

Consider a polynomial,

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

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

p(x+1)=k=0akx+1k

03

Step 3. Value of limx→∞p(x+1)p(x).

Determine the value of limxp(x+1)p(x).

limxp(x+1)p(x)=limxakx+1kakxk=limxx+1xk=limx1+1xk=1k+0=1

So the value oflimxp(x+1)p(x)is1.

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