The linear approximation of f(x)=sqrt (x+1) at a=3 is f(x)=(1)/(4)x-(5)/(4) f(x)=(1)/(2)x-(1)/(4) f(x)=(1)/(4)x+(5)/(4) f(x)=(1)/(2)x-(1)/(2) f(x)=(1)/(2)x+(1)/(2)

## Step 1: Calculate ### We are given and . Therefore, .## Step 2: Calculate ### The derivative of is .## Step 3: Calculate ### Substituting into , we get .## Step 4: Construct the linear approximation### The linear approximation of at is given by . Substituting the values we calculated, we get .