Gokul43201 said:1) Correct
2) (9^x)/(8^x) = (9/8)^x and 9/8 > 1. How does a^x behave if a<1, a=1, a>1 ?
Limits in calculus refer to the maximum or minimum values that a function approaches or reaches as the input (or independent variable) approaches a certain value or approaches infinity. They help to understand the behavior of a function near a particular point on its graph.
To solve limits involving trigonometric functions, you can use the trigonometric identities, such as the sum and difference identities, double-angle identities, and half-angle identities. You can also use the squeeze theorem or L'Hospital's rule, depending on the complexity of the limit.
The formula for solving limits of exponential functions is:
Limit of a^x as x approaches c = a^c, where a is the base and c is the limit value.
Yes, limits involving fractions can be simplified by factoring and canceling common terms. However, if the fraction has a variable in the denominator, you may need to use other techniques, such as multiplying by the reciprocal or applying L'Hospital's rule.
Yes, there are several general approaches to solving limits, including direct substitution, factoring and canceling, using algebraic manipulations, and applying specific rules and theorems such as the squeeze theorem, L'Hospital's rule, and the laws of limits. It is important to understand the properties and techniques of limits to determine the best approach for a specific problem.