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- Find the Limit lim cos(12x-cos(3x)) x->7pie/6Find the following limits. limx->+infinity (sin2x)/(x2+1) limx->+infinity (e-2x cosx) limx->+infinity (e-x+2cos3x)ASAP PLS. Find the following limits that exist and are finite (approach a real number) at the indicated point. Choose the applies. 1. lim x-5/|x-5| + (x-1)1/2 x->5+ 2. lim ((cos-1x+8)1/2)/x3/5+9 x->0 3. lim (3x-2)1/2+(x+1)1/2 x->2/3- 4. Iim (sin3x+π)/πx x-> ∞ 5. lim ((5x4+4)1/2)/3x+2 x-> -∞
- Why does the limit as x goes to 0 of cos(1/x) not exist? Can use two different sequences: xn=1/(n*pi), and yn=2/((2n+1)pi) and show that lim cos(1/xn) ≠ lim cos(1/yn).4. Find the limit, if it exists, or show that the limit does not exist: lim(x,y)→(1,−1) 3^−xy cos(x + y)1. Broadly speaking, what are the Limit Laws, and why do they help us calculate limits?2. In Example 3, there is a step where the function x2 − 1x − 1is changed to x+ 1. But unlike the secondfunction, the first function is undefined at x = 1. How can we justify changing functions this way?3. Explain the flaw in the following calculation:limx→0x2sin(1/x) = (limx→0x2) · (limx→0sin(1/x)) = 0 · (limx→0sin(1/x)) = 0.