
lim cinn) six X>0 lim √4+2-8 to t-2
7. Find the limit. Use L'Hospital's rule if appropriate: > e* + 100x lim x= 3x3 - X
Use L'Hospital's rule to find the limit
lim(3 – x?) x->0
1. Find the limit. lim X00 (e-2x cos(x))
What is the limit definition of the integral cos x dx? lim Σ COS (1): η. lim Σ COS η. (1) (1) lim Σ COS T in Σων (1)
Compute the limit by using known power series
2. lim 30 · (arctan (2) – sin (2)) 1 - cos (22)
8. (i) Find C[F(t)], where F(t) = { if 0 st 34, ift> 4 (ii) Compute the convolution e2 et directly by the definition of the convolution (iii) Evaluate Lle-2445 - e cos(4t) + sin(V2t)). blom.
Use L'Hospital to determine the following limit. Use exact values. In a lim > 1 31n z C Evaluate the limit using L'Hopital's rule lim 8 cos( – 3x)sec(5x)
e-27 2. Calculate L et sint+e-2t cos st sint+e-2 cos 3t+t%e3+ + ✓at ec [e*sin U2n(t) sin 2t sin 21
4. Show that lim -oxsin(1/2) = 0 by by appealing directly to the definition of limit. Recall that -1 < sin < 1. 5. Define a function that is nowhere continuous and another function that is continuous only at one point in its domain.