For a certain function f(x, y). lim-0 f(t, 0) = 0 and lim 0 f(t, 3t) = 0. Does this mean that the limit %3D lim (r,y)-(0,0) f(x, y) exists? True False
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A: Thanks for the question :)And your upvote will be really appreciable ;)
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- Calculate the value of the limit lim(x,y)→(0,0) 22xy/x^2+y^2 as we approach (0,0) along the path γ(t)=(−t,t).Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.
- the limit lim(x,y,z)→(0,0,0)[xy+xz+yz]/[x2+y2+z2]The Michaelis-Menten equation for the velocity v of the enzymatic reaction at the concentration [S] of the S substrate (in the case of the pepsin enzyme) is v = 0.50 [S] 3.0 × 10−4 + [S] What is lim [s] → ∞ v? What does limit mean in this context?compute dy/dx using the limit definition. y = 4 − x2
- a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy limit 0 to ∞ b) Find ∫f(x) dx limit: 1 to 38 if ∫f(x) dx=−17 limit -19 to 1 and ∫f(x) dx=10. limit : -19 to 3815) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10) billion dollars. Assuming that the trends shown in the above models continue indefinitely, calculate the limits lim t→+∞ I(t) and lim t→+∞ I(t)/E(t) algebraically. (If an answer does not exist, enter DNE.) lim t→+∞ I(t) = lim t→+∞ I(t) E(t) = Interpret your answers. In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country. Could the given models be extrapolated far into the future? Yes or NoFind the limit of f(x) as x approaches 2, if it exist. DNE -12 -6 0