The asymptotes of (x²/a²) – (y²/b²) = 1 Show that the vertical distance between the line y = (b/a)x and the upper half %3D of the right-hand branch y = (b/a)Vx² – a² of the hyperbola (x²/a²) – (y³/b²) = 1 approaches 0 by showing that lim * -V - a) = lim (x – V - a) = 0. x→00 Similar results hold for the remaining portions of the hyperbola and the lines y = ±(b/a)x.

Q: 1-z = ? What is lim %3D !- 2!- -2

A: In order to evaluate the limit of a function f(x) at certain point a then replace x by a to get…

Q: 3-v49 B) Without using L'Hopital's rule, find: lim

A:

Q: 1 Find lim +3 using limit rules. 2.

A:

Q: Find the limits in Exercise

A: Given, limx→∞x2+25-x2-1 To find the above limit.

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: (1) limx-ol-cos x 2 sin²x (2) limx-0 x-³…

A:

Q: et +ex -x²-2 Lim- x-0 sin²x-x²

A:

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A:

Q: x* +x + 2x+2 lim x-1 x+1

A:

Q: Use l’Hôpital’s rule to find the limits

A:

Q: Use the Squeeze Theorem to prove lim,e-*arctan(x) = 0.

A: limx→∞e-xarctanx=0 Now, -π2<arctanx<π2                       ∵Range of arctanx is -π2,…

Q: Vx2 – 9 4. lim х-з х — 3 X→3

A: Given limx→3x2-9x-3

Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

Q: In (1 +) lim t1/2

A:

Q: Find the limit. Enter DNE if the limit does not exist. 15zy lim (2,9) → (0,0) 22+ y?

A:

Q: Estimate the limit numerically or state that the limit doesn't exist lim h→0 cos(9/h)

A: We will pick some values for x. Then we will find values of y for those xs.

Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

Q: V5+s-V5 lim s→0 S

A: lims→ 05+s-5s=lims→ 01s+5+5Plug in the value s=0=10+5+5=125

Q: limit as x----0 for the function (px)/(sqrt(bx+a^2))-a using L'Hopitals

A: Apply the limit.

Q: Use limits to determine the equations for all horizontal asymptote.  y = (1 - x2)/( x2 + 1)

A: To find the horizontal asymptote using limit we find the limit of y when x approaches infinity.…

Q: what is lim of x approaches -8 from the left of 7x+56/abolute value of x+8

A:

Q: Estimate the limit numerically. 3x² +270x+5 lim 2x+15 + oo

A:

Q: hey you didnt state the assumptions of the model and the limintations as well

A: To state: Assumptions and limitations of an exponential model.

Q: find the limt for

A:

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

A:

Q: Evaluate the limits with either L'Hopital's Rule or previously learned methods: e*+x2+2x-1 6. lim…

A: Evaluate the limit

Q: L'Haspital X-rileniz lim

A:

Q: y = b Retrieved from:basiccalc_initial_release_13june.pdf 1. lim b 2. lim エ→1.2 3. lim b エ→ー1

A:

Q: Fird the domain of f (x) = 2-Vx2-5 Solve lim x→-3 =? (Don't use L'hopital Rule) x+3

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: find the limit:  limx→∞ (ln x)^3 / x^2

A:

Q: Find the limit analytically: 2-4x lim- 40 5+3x 1.

A:

Q: lim Sint tー 七

A: Given : limt→x2 sintt

Q: Estimate the limit numerically  limx→4 √x−4/x−16=

A:

Q: 3) If lim dt) = 5, can there be a vertical asymptote in the graph of d(f) at t = 0?

A: Given               :  limt→0- d(t)=5   Not Given       :  limt→0 d(t)=? limt→0+ d(t)=?

Q: Estimate the limit numerically or state that the limit doesn't lim 3h _1 h→0

A:

Q: Estimate the limit numerically or state that the limit doesn't exist: lim sec (x) T→1+ vx5–1 (Enter…

A:

Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(12r) lim

A:

Q: How do you evaluate the limit:  limx-->0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

A:

Q: Estimate the limit numerically  limx→4 x^2−2x−8/x^2−3x−4=

A: We have to find limit

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

A:

Q: (х — 2)(г + 2)( +1) (х + 3)(ӕ + 1)

A:

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A: Given:

Q: Find the limit by rewriting the fraction first. x-y+3Vx - 3Vy Vx - Vy lim (х,у)—(0,0) x#y

A:

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: Evaluate the limit sin 7h lim %3D 7h Enter DNE if the limit does not exist. Limit =

A:

Q: Find the limit: limx→0​ x3sin(1/3x​3)

A:

Q: 3-Vx2+9 Without using L'Hopital's rule, find: lim-

A:

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution