x? + x - 2. |x - 1| Let g(x) (a) Find the following limits. (If an answer does not exist, enter DNE.) (1) lim 9(x) 3

Q: (х-а) 2. lim Vx-Va X→a

A:

Q: z2 -6x +36 Find lim I +6 O 36 O 108 The limit does not exist.

A: To find limx→-6x2-6x+36x+6

Q: 2t Q3. Find the value of: lim,-0 tant (x² -1 Q4 Let f(x) ={ 2kx x< 2 x 2 2 Find the value of (k)…

A: 3. to findlimt→02ttant4. to find value of k for the function to be continuousf(x)=x2-1x&lt;22kxx≥2

Q: 1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

A:

Q: Evaluate

A: To evaluate limx→0 e2x-1xSubstituting x=0 , 00 form is obtained Hence , L' Hospital's rule can be…

Q: 3-Vx+3 6. (10) Find lim analytically (if it exists). X→6 X-6

A:

Q: 1. Evaluate the ff. limits: -1 (e*). V1 – e2¤ sin' 2 lim (а) x→0- - 1 - (b) lim x + sin

A: Explanation of the answer is as follows

Q: (x²+5x – 6 Evaluate: lim x-1 А) 5 B limit does not exist (c) 3 D) 7

A:

Q: x² – y? - Show that lim (x, y)→(0, 0) x² + y? does not exist. .2

A: Given: lim(x, y)→(0, 0)x2-y2x2+y2

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: 1 f(x), where f(x) = Find lim x + 10 x→- 10- O A. - 1 O B. ∞ O C. - ∞ D. 0

A:

Q: 3. Find the values of the constants a and b such that Va + bx – V3 - lim x → 0 3.

A:

Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

Q: -xy س3: أحسب lim (x,y)→(0,0) x²+y² إضافة ملف

A: See the attachment

Q: x2 + kx – 10 5. Find the value of k that would make the limit exist. lim f(ax) = x – 2

A: The given limit is limx→2fx=x2+kx-10x-2

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: x³, x 4 b) f(x) = i. lim f(x) X-1+ ii. lim f(x) X+4 iii. lim f(x) x4+

A: To graph the given function first we find the function values at some points in the domain.Then plot…

Q: 6 lim | 3 x² – 32 X+3 X - Enter I for oo, -I for -00, and DNE if the limit does not exist. Limit =

A: We shall find left hand limit first if it doesn't exist then limit not exist, if exist and finite…

Q: 1. Find the limits lim (3x – 1) x-1/3 a) | cos x b) lim x 1 - T lim y--5 5 - v c) 3h +1 - 1 d) lim…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the limits in Exercise

A: limx22-1x

Q: 3. Given the function y = [(x² +2x+ 1]/(x), (x0), find: (a) the limit of y as x approaches positive…

A: Given:  The function y=x2+2x+1x, x≠0 To Find:  a The limit of y as x approaches positive infinity.b…

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: 2. Given the function y = [(x-1)3 – 1]/(x), (x#0), find: (a) the limit of y as x approaches 0. (b)…

A:

Q: e – e-* lim I-0 x2 + 3T

A:

Q: valuate the limit 8x2 – 9x – 9 lim x→-o 7 – 7x – 10x2 E the limit does not exist enter DNE. imit =

A: We have to find limit

Q: y of -4 -2 -2 (a) (1) (b) lim f(x) x-1 2.

A:

Q: 2. メー gu)= - fex) = X üls Is1 3メ-1 احب lim (fog) x メー

A: We have to find limit

Q: -x' B. For f(x)={(x+2)² for -1<x<2,find for x<-1 2x2 for x22 Consider one-Sided Limits to deter a)…

A:

Q: nd the one-sided DNE lim_(x². +x+5) x--5- exists). (If an answer does not exist, enter DNE. Submit…

A: Topic:- limits

Q: Please show step-by-step solutions

A:

Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: 1. lim )Gt h->0 2. lim xZ X-1 X>( X-I

A: here is the solution

Q: True or false? If k &gt; 0, then all solutions of y' = −k(y − b) approach the same limit as t →∞.

A:

Q: - [x² + 2 if x < 2 (x) l(x - 3)2 if x 2 2 (a) Find the following limits. (If an answer does not…

A: Given function:

Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

A:

Q: 3 (а+h)2-За? Algebraically calculate the exact limit: lim h→0 h

A:

Q: x*-16y* lim (x.y)¬(2,1) x2–4y2 A 0 B 00 C Does not exist D None of these

A: Topic - limit

Q: 8 lim r→8 r2 8x Enter DNE if the limit does not exist. Limit =

A: Given limit:

Q: f(8+ h)-f(8) lim h-0 where f(x) = 2x + 5. If the limit does not exist enter DNE. Limit =

A:

Q: Jx-2 %3D F(x) x²+x-6 Does lim F(x) exist? x-2

A:

Q: x+1 If f(x) = Solve to find lim f(x)? %3D Vx2+5-x'

A: Here is complete computation for your limit

Q: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: 8. Find the area of the triangle formed by the x and y-axes and the tangent to the graph of y =. %3D…

A:

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

Q: (p- [d) lim xn x→-0

A: In this question, the concept of limit is applied. Limit The limit formula is employed to calculate…

Q: x2 – 1 t(2) = 1 What is lim t(x)?

A:

Q: Find the limit. |1 + x – 1 5) 5) lim x-0 A) 0 B) Does not exist C) 1/4 D) 1/2

A:

Q: e - -1 i. lim 40 -1+ cos r ii. lim(r* + 1) Find your limits

A: