मुफ्त सीमा कैलकुलेटर
फलन की सीमा (limit) निकालें। x के किसी मान पर फलन की सीमा की गणना करें।
Limit Val
0.000000
सूत्र
Limits of Polynomial Functions
Direct Substitution
For polynomial functions, the limit as x approaches a value c is simply f(c). This is because polynomials are continuous everywhere.
lim(x→c) f(x) = f(c)
Verification
The left and right approach values should agree with the direct substitution result, confirming the limit exists.
हल किया गया उदाहरण
Find lim(x→2) of x² - 3x + 2.
- 01f(2) = (2)² - 3(2) + 2
- 02= 4 - 6 + 2
- 03= 0
- 04Left: f(1.999) ≈ -0.001999
- 05Right: f(2.001) ≈ 0.002001
अक्सर पूछे जाने वाले प्रश्न
What is a limit?
A limit describes the value that a function approaches as the input approaches a particular point. It is the foundation of calculus.
Can you always use direct substitution?
For polynomials, yes. For rational functions, you may get 0/0, which requires algebraic simplification, L'Hopital's rule, or other techniques.
What if the left and right limits differ?
If the left-hand limit and right-hand limit are different, the two-sided limit does not exist. This happens at jump discontinuities.
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