Question 25 of 35beginner🔧 ApplyShort Answer2 marks

If f(x)=x2f(x) = x^2, find f(1.1)−f(1)(1.1−1)\frac{f(1.1) - f(1)}{(1.1 - 1)}.

Correct Answer

To find the value of the given expression, we first evaluate the function f(x)=x2f(x) = x^2 at the specified points. We calculate f(1.1)f(1.1) by substituting x=1.1x = 1.1, which results in (1.1)2=1.21(1.1)^2 = 1.21. Similarly, calculating f(1)f(1) gives us (1)2=1(1)^2 = 1.

Next, we substitute these values into the numerator of the expression. The difference is f(1.1)−f(1)=1.21−1=0.21f(1.1) - f(1) = 1.21 - 1 = 0.21. The denominator is calculated as 1.1−1=0.11.1 - 1 = 0.1.

Finally, dividing the numerator by the denominator yields the result. The calculation is 0.210.1\frac{0.21}{0.1}, which simplifies to 2.1. Thus, the value of the expression is 2.1.

Exercise: Miscellaneous Exercise on Chapter 2 | Q: 2 | (Page 17)
For More Understanding

Explanation

The question requires evaluating a function f(x)=x2f(x) = x^2 at specific points and simplifying the resulting expression. The context provides the definition of the function in the Miscellaneous Exercise section. Although the specific solution steps are not explicitly written in the provided text chunks, the method of evaluating functions by substitution is demonstrated in Examples 16, 17, and 22 (e.g., finding f(−4)f(-4) or f(1)f(1)). By substituting x=1.1x=1.1 and x=1x=1 into the function f(x)=x2f(x)=x^2, we find the values required to solve the problem.

Solution Steps

  1. Step 1: Identify the function given: f(x)=x2f(x) = x^2.

  2. Step 2: Calculate the value of the function at x=1.1x = 1.1. We have f(1.1)=(1.1)2=1.21f(1.1) = (1.1)^2 = 1.21.

  3. Step 3: Calculate the value of the function at x=1x = 1. We have f(1)=(1)2=1f(1) = (1)^2 = 1.

  4. Step 4: Substitute these values into the numerator: f(1.1)−f(1)=1.21−1=0.21f(1.1) - f(1) = 1.21 - 1 = 0.21.

  5. Step 5: Calculate the denominator: 1.1−1=0.11.1 - 1 = 0.1.

  6. Step 6: Divide the numerator by the denominator: 0.210.1=2.1\frac{0.21}{0.1} = 2.1.

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