AP EAMCET · Maths · Limits
If \(\quad f: R \rightarrow R \quad\) is defined by \(f(x)=[x-3]+|x-4|\) for \(x \in R\), then \(\lim _{x \rightarrow 3^{-}} f(x)\) is equal to
- A \(-2\)
- B \(-1\)
- C \(0\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
Given that, \[ \begin{aligned} f(x) & =[x-3]+|x-4| \\ \therefore \lim _{x \rightarrow 3^{-}} f(x) & =\lim _{x \rightarrow 3^{-}}([x-3]+|x-4|) \\ & =\lim _{h \rightarrow 0}([3-h-3]+|3-h-4|) \\ & =\lim _{h \rightarrow 0}([-h]+1+h) \\ & =-1+1+0=0 \end{aligned} \]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The point \((3,4)\) is the focus and \(2 x-3 y+5=0\) is the directrix of a parabola. Its latusrectum isAP EAMCET 2015 Easy
- The point \(\mathrm{P}(2,1)\) is translated to a point \(\mathrm{Q}\) parallel to the line \(L \equiv x-y-4=0\) by \(2 \sqrt{3}\) units. If the point \(Q\) lies in the third quadrant, then the equation of the line passing through \(\mathrm{Q}\) and perpendicular to \(\mathrm{L}\) isAP EAMCET 2023 Hard
- The circum radius of the triangle formed by the points \((2,-1,1),(1,-3,-5)\) and \((3,-4,-4)\) isAP EAMCET 2025 Medium
- The distance from the origin to the image of \((1,1)\) with respect to the line \(x+y+5=0\) isAP EAMCET 2016 Easy
- \(\int \frac{x}{x^3-3 x+2} d x=\)AP EAMCET 2018 Medium
- \([\mathrm{x}]\) represents the greatest integer function.
If \(\lim _{x \rightarrow 0^{+}} \frac{\cos [x]-\cos (k x-[x])}{x^2}=5\) then \(k=\)AP EAMCET 2025 Hard
More PYQs from AP EAMCET
- If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined as \(f(x)=\frac{x^6}{x^6+2020}\), \(\forall x \in \mathbf{R}\), then the range of \(f\) is .......AP EAMCET 2020 Easy
- If , defined below, is continuous at thenAP EAMCET 2021 Medium
- \(A\) and \(B\) are two events such that \(P(A)=0.58\), \(P(B)=0.32\) and \(P(A \cap B)=0.28\). Then the probability that neither \(A\) nor \(B\) occurs isAP EAMCET 2018 Easy
- A buffer solution is prepared by mixing \(10 \mathrm{~mL}\) of \(1.0 \mathrm{M}\) acetic acid and \(20 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) sodium acetate and then diluted to \(100 \mathrm{~mL}\) with distilled water, The \(\mathrm{pH}\) of the buffer solution is ( \(\mathrm{p} K_a\) of acetic acid is 4.76 )AP EAMCET 2019 Medium
- Consider the following
A) 0.0025
B) 500.0
C) 2.0034
Number of significant figures in \(\mathrm{A}, \mathrm{B}\) and C respectively, areAP EAMCET 2025 Easy - The acute angle between the lines whose direction cosines are given by the equations \(l+m+n=0\) and \(2 l m+2 l n-m n=0\) isAP EAMCET 2018 Medium