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Question 1. Calculate the following limits, justifying your answers carefully. 20 (a) lim 1+-2.13 + 5...
1. Compute the following limits algebraically, if possible: 4.2 +1-3 (a) lim 5.2 – 1 (b) lim 2 - 2 100 3.42 - 2.c 2 (c) lim csc(7x) sin(4x) (d) lim lim (1+3) 20 22 (e) lim +01 – COS X
solve d-f
Find the limits and show your work. Use L'Hospital's Rule where appropriate. (a) lim-0 tan 3.0 2.2 1 (b) limu+0+ In(X) (c) limx→ In(x + 3) – In(3x + 2) (d) limz+ x sin(5) (e) lim.+ 22-45 4" +3: (f) limo (#2) (g) lim + (e+ + a)*
Q3. Find the following limits: x1 x+1 (b) lim (c) lim X-3 X-2
Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a > 0, . limn-oo a = 0, or a < 0, How does this accord with the various convergence theorems?)
Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a...
2.c)
2. Show that each of the following limits does not exist : (a) lim 1 + 2y (b) lim (2 + y) (x,y)--(0,0) -y (2.) +0,0) r? + y2 (d) 6ry lim (x,y)+(0,0) 24 + y (c) lim (x,y)0,0) - 2 + y
i need help with #6, #15, and # 17. please and thank
you!
1 lim 8 lim- 22 2 lim Problems for $1.3 For problems 1 through 14: By replacing functions with a few terms of their asymptotic series, find the following limits. et - 26 +1 tan(x) – sin(x) cosh(x) 20 cos(2) - 11 - 22 9 lim sin(x) sin (x) – 2,2 1-0 24 *+0 tan(x) tan-(x) - 22 3 lim x2 + x -2 10 lim x1...
1. Determine if the following limits exist. In each case prove and explain your argument. (c) lim x +y + y sin x siny *(0,0) XY lim x-(0,0) x4 + y2 lim x+(0,0) x2y2 + (x + y2)2
Evaluate the following limits. If you use L'Hopital's Rule, indicate on your paper that you have done so. If a limit is oo or - 0, then write oo or -oo. You may write DNE for does not exist. x² – 1 a.) lim Preview 7+1 In 4.q7 = - b.) lim 1+ I-4 2 – 3. - 4 Preview et -1 c.) lim 1+0 - sin(4x) Preview d.) limsin 4x = Preview Preview
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+
40 Show the following results. 1-e2...
Question 4 4.1 Express the limit as a definite integral on the given integral: 1-x} Ax , [2,6] lim Σ=1 a. (2 Marks) n->00 4+x} lim (?-1 - Ax ,[1,3] (xi) - 4 b. (2 Marks) n->00 4.2 Evaluate the following expressions. Show your calculations. $=1(2p – p2) b. En-o sin a. (2 Marks) пп (2 Marks) 2 C. 2m +2 53 Lm=1 3 (2 Marks) [Sub Total 10 Marks]