The following limit can be broken down to much simpler limits using the properties of limits. Identify two ofthese properties and explain how they are fitting. Lim x aproaching 2 for (-4.9t^2)+3.5t+1
here are the properties of limits: How can two of them apply?
http://www.analyzemath.com/calculus/limits/properties.html
The given limit is \<lim(x→2) (-4.9t^2) + 3.5t + 1\>. To simplify this limit using the properties of limits, let's break it down step by step.
1. **Sum Rule**: The sum rule states that if you have a limit of the sum of two functions, you can take the limit of each function separately and then add the results. In this case, we have (-4.9t^2) + 3.5t + 1. We can apply the sum rule by taking the limits of each term separately.
- First term: \<lim(x→2) (-4.9t^2)\> can be simplified separately.
- Second term: \<lim(x→2) (3.5t)\> can also be simplified separately.
- Third term: \<lim(x→2) (1)\> is a constant, so its limit is itself.
2. **Product Rule**: The product rule states that if you have a limit of the product of two functions, you can take the limit of each function separately and then multiply the results. However, we do not have a product of functions in this case, so we won't be applying this rule here.
Now, let's simplify each term separately:
- For the first term, \<lim(x→2) (-4.9t^2)\>, we can substitute `x` with `2` since the limit is approaching `2`. By doing so, we get \<-4.9(2)^2\> which becomes \<-4.9(4)\> and simplifies to \<-19.6\>.
- For the second term, \<lim(x→2) (3.5t)\>, we substitute `x` with `2` again. This gives us \<3.5(2)\> which simplifies to \<7\>.
Finally, we add the results of each term:
\<lim(x→2) (-4.9t^2) + 3.5t + 1\> becomes \<-19.6 + 7 + 1\> which simplifies to \<-11.6\>.
Therefore, the simplified form of the given limit is \<-11.6\>.