. Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

Q: 3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

A: The given rational function is 3x2+x2y2+3y2+3z2x2+y2+z2. Evaluate the limit along the line y=0,z=0.…

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: Find lim (1 + sin5x) cot3x x-0+

A:

Q: A. Evaluate the following: NO Differentiation 1. lim(x³ - 2x² + 3x-1) x->2 2 lim (4 + 3r²-2r+5)

A: To evaluate the limit of the given function

Q: tan(sin(ra)) tan(т(»—100)) Find lim

A: The objective is to evaluate the limit.

Q: Find lim(2 – x)tan(r2/2)

A:

Q: 1 2. Lim x0x 1 sin x

A: Given:      limx→0+1x-1sinx simplifying we get     =limx→0+sinx-xxsinx Apply L'Hospital's Rule:…

Q: Find the value of lim sec 3. 2 Select your answer. 2/3 3 3 2/3 +3 3 2/3 – 3 3. 2/3 3 3

A:

Q: S e?+tdt lim 2-40 sin(2x) +

A:

Q: 1. 5.lim cos(x) sin(x)

A:

Q: For what values of a and b does lim x→0 a = b = sin (2x) x³ +a+ b 2/2) = x² = 0?

A:

Q: 2x x-0 sin 1x f. lim

A:

Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: (x-sin x) A- Find lim,-0 1-cos X/

A:

Q: Let s(x)=sin(x)/x. Explain why it is true that Lim (X-> 2pi) s(x)=0

A: Let  sx=sinxx Explain why it is true that limx→2πsx=0

Q: Show that lim x|cos )= = 0.

A:

Q: Find the value of : sin3x lim x→0 2x

A: This question is based on Limits.

Q: 1f. lim (tanx)x x-&gt;0+

A: Given,

Q: (x² - 3) 7. Build a table to estimate lim sin x

A:

Q: (d) Apply the Squeeze Theorem to verify that lim x² sin I-0 (-1). = 0.

A: SQUEEZE THEOREM-:  Let  f , g and h be functions defined on an interval I . Suppose that for every x…