What are the values of a and B if lim y (1) = 0? I 00 O A) a = -1 and B=0 O B) a = -1 and B= 1 a = 1 and B=-1 O D) a = 0 and B=-1 Q = 1 and B = 1

Q: 5. Prove lim,40 V2r +I= 1.

A: Given :limx→02x+1=1

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: evaluate using Theorem 2 as necessary.

A:

Q: Find the limits

A:

Q: Evaluate using Theorem as necessary.

A: Given : The limit is limt→0 sin2tt .

Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

A:

Q: What is lim m→0 sin(m) m ?

A:

Q: If lim (x,y)→>(a,b) True False f(x, y) L and f is defined at (a, b), then f(a, b) = L.

A: The give statement, If limx,y→a,bfx,y=L and f is defined at a,b, then fa,b=L

Q: Find the limits in Exercise

A: To find the limit of

Q: b. By the definition S'(x) = lim {r + h) – {(x) Verify that f (r) = sec r tan r if f(r) = sec r.

A:

Q: Find the limit. sin?(9x) lim

A: L’Hospital’s Rule : If  limx→af(x)g(x) = 00 or ∞∞  (indeterminate forms) then  limx→af(x)g(x) =…

Q: limits is ideal?

A: To find the width: Calculate the range of the entire data set by subtracting the lowest point from…

Q: By using Sandwich Theorem, prove that lim sin x x-0 r

A: We have to prove that limx→0sin xx = 1 using sandwich theorem. Sandwich theorem states that- Suppose…

Q: Construct a table to find the indicated limit.

A: let f(x)= limx→0 sinx2x

Q: What do the plots in Problem 4 suggest about lim_ u (x,t)? Is this physically reasonable? Explain.

A:

Q: For B = – lim r² -1 6 sin z which one is B?

A: In this question we have the limit for B.

Q: . Use the Squeeze Theorem to determine the value of limx sin

A: To evaluate the given limit limx→0x4sinπx by using the Squeeze theorem. Now, the Squeeze thorem…

Q: O Find lim (X,Y)→ LD,0) **+3y* or show it DNE.

A:

Q: 3 Prove limx = 00 by the definition.

A:

Q: Find the limit: 4x4 – 4y? lim (r,y) → (4,4) x² – y?

A:

Q: Evaluate: lim, (cos z). Show your solution. O -1

A: Limit of a function f(x) at point x = a exists only when Left hand Limit(LHL) = Right hand limit…

Q: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

Q: Find the limits in Exercis

A: On directly substituting the limit, indeterminate form 00 is obtained. So, to find the limit, we…

Q: 4. If tige Lim, show that fg & LUM.

A:

Q: - lim a sin

A: We have to find limit using l'Hospital Rule

Q: lim = 0 sin x.

A: limx→01x-1sinx=0

Q: Find the limits in Exercis

A: We can find the limit of an expression by applying the limit point to the variable in the expression…

Q: lim (sin r)tan z T/2

A: Given problem :- Identify the indeterminate form and evaluate limx→π-2sinxtanx

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Evaluate: lim sin(3x)cot(2x) O a. 2 O b. 3 2 O c. 3 O d. 2 3

A: limx→0 sin3xcot(2x) limx→0sin(3x)cos(2x)/sin2x so now it form 0/0 so we use la'hospital rule…

Q: I. Apply the different techniques in evaluating the each item, you have to show your work at each…

A:

Q: Find the limit 10xy lim (2,y) → (21, y1 ) 25x2 y2 at the following points. - 10xy lim (a,y) → (0,11)…

A:

Q: Evaluate the following limits: 1 1 (i) lim{ sin -+cos- X X 1/x 1/x +a, 1/x a1 + (ii) lim ..... ,a1…

A:

Q: Use the Squeeze Theorem to determine the value of limx? cos(=-

A:

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: The ratio test: {en =Tan+1/anl, p = %3D lim Po}. If p> 1 use a different test. True False

A: We will first state ratio test Then we will use the definition of ratio test to determine whether…

Q: Find the limit. lim sin P-(8, 0, -8) TT 1, OOO

A: To find the limit:                          limP→8,0,-8ey2sin-1-zx

Q: Prove that lim sin( nx) + n dx= In 2 . (n+) Explain your answer carefully

A:

Q: Use a graphing utility to graph the fur 6 sin(r) lim

A:

Q: Find the limit of the trigonometric function.

A: Given: limx→7  secx6

Q: nd lim delta -> -4, tan(delta + 4) /5delta+20

A:

Q: (1 cosrjir lim,o = ?

A:

Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: (b) Show that lim (z.)(0,0) lim (z.)(0,0) does not exist. (c) Show that does not exist if +: 0, p…

A:

Q: is lim (sec x)ot æ 2

A: Apply exponent rule

Q: Evaluate using Theorem 2 as necessary.

A:

Q: Why does lim sec x = – o? How is this related the triangle in the drawing below? Explain. Adjacent

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given limx→0sinxsecxx

Q: If lim f(x, y) =and fis defined at (a, b) then f(a, b) = L (r,y) (a,b) O True O False

A: True.

Q: Let a > 0 be a real number. Prove that lim x“ sin = 0.

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: