Question

In: Math

find the limit as k approaches infinity of [1+(1/10^k)]^10k step by step using the l'hospital

find the limit as k approaches infinity of [1+(1/10^k)]^10k

step by step using the l'hospital

Expert Solution

we are given

Let's expression as y

now, we can take ln on both sides

now, we can apply L'hospital rule

we can find derivative of top and bottom term

we can apply L'hospital rule again

when we plug k=inf

we get inf/inf

so, we can apply L'hospital rule again

now, we can plug k=inf

now, we can find y

So, we get

............Answer

milcah answered 2 years ago

Use a graphing utility to complete the table and estimate the limit as x approaches infinity....

Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then use a graphing utility to graph the function and estimate the limit. Finally, find the limit analytically and compare your results with the estimates. (Round your answers to one decimal place.) \(f(x)=x^{2}-x \sqrt{x(x-1)}\)x10^(0)10^(1)10^(2)10^(3)10^(4)10^(5)10^(6)r(x)

Can you apply L'Hopital's rules to the following limit? lim x approaches infinity (1+cos(x)) / sin(x)...

Can you apply L'Hopital's rules to the following limit? lim x approaches infinity (1+cos(x)) / sin(x) true or false

Answer all parts of question 1. 1a.) Find the limits, as t approaches both positive infinity...

Answer all parts of question 1. 1a.) Find the limits, as t approaches both positive infinity and negative infinity, of the solution Φ(t) of the ivp x' = (x+2)(1-x^4), x(0) = 0 1b.) Find the value of a such that the existence and uniqueness theorem applies to the ivp x' = (3/2)((|x|)^(1/3)), x(0) = a. 1c.) Explain why x' + ((sin(t)) / ((e^t) + 1)) * x = 0 cannot have a solution x(t) such that x(1) = 1 and...

(a) Find the limit of the following functions: -lim as x approaches 0 (1-cos3(x)/x) -lim as...

(a) Find the limit of the following functions: -lim as x approaches 0 (1-cos3(x)/x) -lim as x approaches 0 (sin(x)/2x) -lim as theta approaches 0 (tan (5theta)/theta) (b) Find the derivative of the following functions: -f(x) = cos (3x2-2x) -f(x) = cos3 (x2/1-x) (c) Determine the period of the following functions: -f(x) = 3 cos(x/2) -f(x)= 21+ 7 sin(2x+3)

lim x approaches infinity of (6x^3+11x^2+12)^(1/ln(x)

−7, 8, 8, 6, 10 find the variance step by step

From Starbucks Corp form 10k ( 10-K reports on SEC.GOV and most recent two years report...

From Starbucks Corp form 10k ( 10-K reports on SEC.GOV and most recent two years report should be used for some ratio analysis ) Balance Sheet Using the 10-K, show that the fundamental accounting equation, Assets = Liabilities + Stockholders' Equity, is true for your company at the end of the most recent year-end. A _______= L __________+ S.E. _____________ What was your company's largest asset (net) at the end of the most recent year? List the types of assets...

Ratio Analysis *From Starbucks Corp form 10k ( 10-K reports on SEC.GOV and most recent two...

Ratio Analysis *From Starbucks Corp form 10k ( 10-K reports on SEC.GOV and most recent two years report should be used for some ratio analysis ) Calculate your company's gross profit rate for the past two years. Did they increase or decrease? Explain the meaning of the change. Calculate your company's account receivable turnover, inventory turnover for the past three years. What does the trend suggest to you about the company Calculate the company's return on equity (ROE) for the...

f(x) = sec x - 1 / x^2 to find the limit using rationilization

How do you find/calculate division wide data using a 10k and or FSAP report? if you...

How do you find/calculate division wide data using a 10k and or FSAP report? if you can't do so with either please explain what forms or calculations youi do need to find the information