Question 11 of 70beginner🔧 ApplyNumerical1 mark

Evaluate the following limits in Exercises 1 to 22. lim⁡x→1ax2+bx+ccx2+bx+a,a+b+c≠0\lim_{x \to 1} \frac{ax^2 + bx + c}{cx^2 + bx + a}, a + b + c \neq 0

Correct Answer

1

Exercise: EXERCISE 12.1 | Q: 11 | (Page Page 21)
For More Understanding

Explanation

Since the function is a rational function and both numerator and denominator are polynomials, we can evaluate the limit by direct substitution if the denominator is non-zero at the point. At x=1, numerator = a+b+c and denominator = a+b+c, which is non-zero by given condition. Therefore, the limit equals 1.

Solution Steps

  1. Step 1: Substitute x = 1 into the numerator: a(1)^2 + b(1) + c = a + b + c.

  2. Step 2: Substitute x = 1 into the denominator: c(1)^2 + b(1) + a = c + b + a = a + b + c.

  3. Step 3: Since a + b + c ≠\neq 0, the denominator is non-zero, so the limit is (a+b+c)/(a+b+c) = 1.

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