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Infinite Limits : In this section we will see limits whose value is infinity or minus infinity.
The primary thing we have to probably do here is to define just what we mean while we say that a limit contain a value of infinity or minus infinity.
Definition
We say
If we make f(x) arbitrarily large for all x adequately close to x=a, from both of the sides, without in fact letting x = a .
if we can make f(x) arbitrarily large & negative for all x adequately close to x=a, from both of the sides, without letting x= a actually.
These definitions can be modified appropriately for the one-sided limits as well.
Let's start off with a typical example showing infinite limits.
The sum of the diameters of two circles is 2.8 m and their difference of circumferences is 0.88m. Find the radii of the two circles (Ans: 77, 63) Ans: d 1 + d 2 = 2.8 m=
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
what is the LCM of 4, 6, 18
if 500kg of food lasts 40 days for 30 men.how many men will consume 675kg of food in 45 days.
Use the definition of the limit to prove the given limit. Solution Let ε> 0 is any number then we have to find a number δ > 0 so that the following will be true. |
Some Definitions of e 1. 2. e is the unique +ve number for which 3. The second one is the significant one for us since that limit is exactly the limit
Interval of Convergence After that secondly, the interval of all x's, involving the endpoints if need be, for which the power series converges is termed as the interval of conv
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1+1
Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th
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