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Tarun Gehlot
Works at T.G TUTORIALS
Attended MBM Engineering College
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Tarun Gehlot

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chapter 15 Worked Out Examples 6
   Example:  8    Evaluate the following limits: (a)   (b)   (c)   (d)   (e)   Solution:  8-(a) Notice that as  ,  , that is ,   has no particular limit to which it converges. Hence   keeps oscillating between  and  as   becomes smaller and smaller, i.e.,  ...
   Example: 8   Evaluate the following limits: (a) (b) (c) (d) (e)  Solution: 8-(a) Notice that as , , that is ,  has no particular limit to which it converges. Hence  keeps oscillating between and as  becomes smaller an...
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chapter 13 Worked Out Examples 4
   Example:  6      Evaluate the following limits: (a)   (b)   (c)   (d)   Solution:  6 The limit is of the indeterminate form  , but can be reduced into a combination of two standard limits as follows: Solution:  6-(b)  can be expanded as  Hence, Solution:...
   Example: 6     Evaluate the following limits: (a) (b) (c) (d)  Solution: 6 The limit is of the indeterminate form , but can be reduced into a combination of two standard limits as follows: Solution: 6-(b)  can be ...
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chapter 11 Worked Out Examples 2
   Example:  3     Find the values of   and   if  Solution:  3 The limit can be rearranged as Since the limit is finite, the coefficient of   has to be necessarily  . Therefore,      Example:  4      Evaluate   where   represents the greatest integer functi...
   Example: 3    Find the values of  and  if  Solution: 3 The limit can be rearranged as Since the limit is finite, the coefficient of  has to be necessarily . Therefore,      Example: 4     Evaluate  where  repre...
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chapter 9 Methods for Evaluation of Limits 2
  (C) RATIONALIZATION In this method, the rationalization of an indeterminate expression leads to determinate one. The following examples elaborate this method. (i)   Rationalizing both the numerator and the denominator  A determinate form Cancelling out   ...
 (C) RATIONALIZATION In this method, the rationalization of an indeterminate expression leads to determinate one. The following examples elaborate this method. (i)  Rationalizing both the numerator and the denominator  A d...
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chapter 7 Some Standard Limits 3
(G)   This is an extension of the previous limit as follows: (H)   We have seen the limits   and   . How can we use these limits to derive the limits that we require now Consider   . Substituting   gives  . Also, as  Hence, our limit reduces to  Similarly, ...
(G)  This is an extension of the previous limit as follows: (H)  We have seen the limits  and  . How can we use these limits to derive the limits that we require now Consider  . Substituting  gives . Also, as  Hence, ou...
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chapter 5 Some Standard Limits 1
(A)   Both the limits above are indeterminate, of the form  . We are discussing here a geometric interpretation of these limits. Consider a sector   of a unit circle as shown in the figure below. We see that  or  or What happens as   decreases or as  We see...
(A)  Both the limits above are indeterminate, of the form . We are discussing here a geometric interpretation of these limits. Consider a sector  of a unit circle as shown in the figure below. We see that  or or What hap...
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chapter 14 Worked Out Examples 5
     Example:  7    Evaluate the following limits: (a)   (b)   (c)   (d)   (e)   Solution:  7-(a) Notice that all the limits above are of the form   where  and   that is, these limits are of the indeterminate form  . In Section –  , we saw how to evaluate s...
     Example: 7   Evaluate the following limits: (a) (b) (c) (d) (e)  Solution: 7-(a) Notice that all the limits above are of the form  where and  that is, these limits are of the indeterminate form . In Section – , we ...
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chapter 12 Worked Out Examples 3
     Example:  5      Evaluate the following limits: (a)   (b)   (c)   (d)   Solution:  5-(a) Before proceeding to solve these limits, it should be mentioned that most limits can be evaluated in more than one manner. (In fact, L’Hospital’s rule is a techniq...
     Example: 5     Evaluate the following limits: (a) (b) (c) (d)  Solution: 5-(a) Before proceeding to solve these limits, it should be mentioned that most limits can be evaluated in more than one manner. (In fact, L’H...
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chapter 10 Worked Out Examples
     Example:  1    Evaluate the following limits (a)   (b)   (c)   Solution:  1-(a) This limit is of the indeterminate form  . Combining the two dfractions in this limit should lead to a cancellation of the factor giving rise to this indeterminacy, i.e.  C...
     Example: 1   Evaluate the following limits (a) (b) (c)  Solution: 1-(a) This limit is of the indeterminate form . Combining the two dfractions in this limit should lead to a cancellation of the factor giving rise to...
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chapter 8 Methods for Evaluation of Limits
Now we discuss the various methods used in obtaining limits. Each method will be accompanied by some examples illustrating that method. (A) DIRECT SUBSTITUTION This already finds mention at the start of the current section, where we saw that for a continuou...
Now we discuss the various methods used in obtaining limits. Each method will be accompanied by some examples illustrating that method. (A) DIRECT SUBSTITUTION This already finds mention at the start of the current section,...
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chapter 6 Some Standard Limits 2
(C)   This limit is of the indeterminate form   . We can easily evaluate this limit based on the previous limit. (Property of log) This limit can alternatively be evaluated by using the expansion series for   (All other terms involving   tend to  This is ju...
(C)  This limit is of the indeterminate form  . We can easily evaluate this limit based on the previous limit. (Property of log) This limit can alternatively be evaluated by using the expansion series for   (All other ter...
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chapter 4 Rules for Evaluation of Limits
Now that we’ve had an intuitive introduction to limits, how do we go about evaluating limits for arbitrary functions For example, consider  . How does this function behave as   (This, as we have seen in the previous section, is an indeterminate form). Befor...
Now that we’ve had an intuitive introduction to limits, how do we go about evaluating limits for arbitrary functions For example, consider . How does this function behave as  (This, as we have seen in the previous section, i...
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Respected teachers ,Dear students ,friends , brothers &  sisters .  I work as a statistical consultant / maths teacher /civil engineer / consultant / analyst .
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My  Expertise Areas

1. complex analysis
2. lap lac and Fourier transforms
3. advanced abstract algebra
4. specials functions
5. topology
6.advanced calculus analysis
7. Lebesgue measures and integration
8. structural analysis
9. differential geometry 
10.numerical analysis
11. elementary mechanics 
12. linear programming logic
13. analytically geometry problems
14. vectors analysis
15.fluid mechanics 
16. mathematical statics 
18. tensor calculus
19. real analysis
20 logical maths and logics of maths in space science
21 space frames
22 numerical techniques
23 vibration analysis
24 measure theory
25 finite element methods
26 non linear functions
27 cryptography
28 Elementary Harmonic analysis
29 Distribution Theory:
30 tangent and cotangent spaces;
31 Probability Theory and Mathematical Statistics
32 Design of Experiments
33 Sampling
34 Modern Regression
35 Survival Analysis
36 Survey Psycho metrics
37 Statistical Inference
38 application of statistics and mathematics

Education
  • MBM Engineering College
    B.E (Civil Engineering ) (Honors ), 2008 - 2012
  • MBM Engineering College
    M.E . ( Structure Engineering ), 2012 - 2014
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