JICHFIXO. SOLVE STEP BY STEP IN DIGITAL FORMAT DONT USE CHATGPT For Exercises 7-18, evaluate the given limit. 10. 12. ご支援ありがとうございました 14. xy2 x2 + y4 xy2 lim (x,y)-(0,0) x2 + y2 lim (x,y)-(0,0) lim (x,y)-(0,0) x² - 2xy + y² x-y
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- Estimate the limit numerically or state that the limit doesn't existlim h→0 5^h−1/h=Does the limit lim(x,y)->(0,0)(x4 -4y2)/(x2+2y2) exist. Explain your answer.Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim h→0 8h2 + h 3h2 + 3h - ________________ If the limit does not exist, say why. (If the limit does exist, so state.) -The limit does not exist because one side diverges to ∞ and the other side diverges to −∞. -The limit does not exist because only one of the left or right limits exists as a finite value. -The limit does not exist because the left and right limits exist but are not the same finite value. -The limit does not exist because it diverges to ∞ or −∞. -The limit does exist and is a finite number.
- Prove that the limit of xy[(x^2 - y^2)/(x^2 + y^2)] is zero as (x, y) goes to (0,0)Investigate the limit numerically and graphically. lim?→±∞8?+14?2+9‾‾‾‾‾‾‾‾√limx→±∞8x+14x2+9 Calculate the values of ?(?)=8?+14?2+9‾‾‾‾‾‾‾‾√f(x)=8x+14x2+9 for ?=±100,x=±100, ±500,±500, ±1000,±1000, and ±10000.and ±10000. (Use decimal notation. Give your answers to six decimal places.) ?(−100)=f(−100)= ?(−500)=f(−500)= ?(−1000)=f(−1000)= ?(−10000)=f(−10000)= ?(100)=f(100)= ?(500)=f(500)= ?(1000)=f(1000)= ?(10000)=f(10000)= Graph ?(?)f(x) using the graphing utility. ?(?)=f(x)= 8x+1√4x2+9 powered by What are the horizontal asymptotes of ??of f? (Give your answer as a comma‑separated list of equations. Express numbers in exact form. Use symbolic notation and fractions where needed.) horizontal asymptote(s):Find the following limits. Show your work. limit as x approaches infinity. A.) 3-7x^5/x+6 B.) limit as x approaches infinity ( radical x^2+3 - radical x^2-5) C.) limit as x approaches infinity radical x^4-6x^3-5/5x^2+4
- Evaluate the limit lim z→2+i [(z−1)(3−2i)+1−3i] and use the definition of the limit (−δ) to verify this limit.1. Why is L’Hosipital’s rule useful for finding the limits? Can it be used in every situation? Please justify your answer? 2. Evaluate each limit. Use L’Hospital’s Rule where appropriate.(i) lim?→3 ?3−27 ?2−3 (ii) lim?→1 ?2+8?−9 (?−1)In the theory of relativity, the Lorentz contraction formula ______________L =L0 √ 1 - v2/c2 expresses the length L of an object as a function of itsvelocity with respect to an observer, where L0 is thelength of the object at rest and c is the speed of light. Find limv->c Land interpret the result. Why is a left-hand limitnecessary?