Approximate 193^5√ , correct to one decimal place, by using a sequence of values that gets closer and closer to 5–√ .(1 point)
To approximate 193^5√ to one decimal place, we can use a sequence of values that gets closer and closer to 5–√. We will start with an initial guess and improve upon it iteratively.
Let's start with an initial guess of 4.5 for 5–√:
- When we substitute this value into the expression, we get: 193^(4.5)√.
- To improve the approximation, we can increase the value of the exponent to get closer to 5.
Next, we can try a value of 4.6 for 5–√:
- When we substitute this value into the expression, we get: 193^(4.6)√.
Again, to improve the approximation, we can increase the value of the exponent.
Continuing this process, we can keep trying values that are increasing and getting closer to 5.
Eventually, we will reach a value that approximates 193^5√ to the desired accuracy of one decimal place.