Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6  f(x) = L, and prove that the limit is correct by completing a δ − ε proof for the limit of the function

Q: Find limit of lim x-->0 of f(x)= (e3x-3x-1)/(4x^2

A: Given limx→0e3x-3x-14x2

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

A:

Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

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

A:

Q: Evaluate the limit algebraically. 4x lim x→5 5 + x5 If the limit does not exist enter DNE. Limit =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

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

A: Given: limx→2x-2ln3x-5 Here we get an indeterminate form, Therefore by using the L-Hospital rule,…

Q: Calculate the limit limx→13√x−1x−1.

A:

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

A: Here it is required to estimate the limit numerically to two decimal places.

Q: Use the definition of the limit of a function of two variables to verify the limit.

A:

Q: Find the limit, if it exists.

A: Consider the given: limx→∞ x21−8x2Divide numerator and denomintor by "x2",limx→∞ x21−8x2=limx→∞…

Q: Find the limit limx→0ax−1x.

A: Given, The limit is,

Q: Evaluate the limit: lim (x - Inx)* x→0+

A: Using limit definition

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

A:

Q: Evaluate the limit |x – 4| lim x-4 x- 4 If the limit does not exist enter DNE. Limit =

A: →For existance of limit at any point,         Left hand limit(LHL) and right hand limit(RHL) at that…

Q: Find the limit. lim (5x + 4x + 3) X--3

A:

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

A: We have to evaluate the following limit: limx→2x-2ln3x-5 The above limit is in 00 form. Therefore we…

Q: The value of the limit x42x-3 lim メー)イ X-イ

A: Given : limx→1x2+2x-3x-1

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: Show that the limit lim- X0 X does not exist

A:

Q: Determine the infinite limit. X 1 lim x4+ X - 4 -CO

A: We will plug x=4^+ in the expression first. We got 0 in denominator. So lets check by plugging…

Q: lim x" x→0+

A:

Q: Use l'Hopital's rule to find the limit. (√x² + 4x - x) 51) lim X→00

A: Given; Limx-infinity [sqrt(x2+4x) -x]. Repost the next question.

Q: find the given limit  lim(-x^2+6x-3) x-->7

A: We need to find the value of the given limit

Q: Evaluate the limit |x lim x+6 x - 6 - 6| If the limit does not exist enter DNE. Limit =

A: Evaluate the limit

Q: Calculate the limit if it exists: lim x→4 for 5/(x-4)2

A:

Q: Determine the infinite limit. limit as x approaches 3 from the right side of ln(x2-9)

A: We have ln(x2 - 9 ) if we take x as √10 which is approximately equal to 3.16, then, x2 - 9 =1…

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

A: limx→23x−95x−25 Since we have an indeterminate form of type 00 Apply the L' Hospital's rule:…

Q: 4) Determine the limit. lim 1 f(x), where f(x): X + 10 X-- 10-

A: Given, f(x)= 1/(x+10)

Q: Compute the limit: lim (1+3x)^(-5/x) x→0

A: We have to evaluate the given limit.

Q: Evaluate the limit algebraically. 1 х — 4 - lim x→4 x + 4 x2 – 16 If the limit does not exist enter…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Prove that lim 4x – 2 = 10 using the epsilon-delta definition of a limit.

A: Let, ε>0 is any number. and δ>0 is also a number. For the given limit, fx=4x-2a=3L=10 From ε-δ…

Q: How do you approximate a limit numerically AND graphically?

A: We always evaluate limits from both the left and right directions and if they match, then, the limit…

Q: Find the limit: limx 1(x2 + x + 2)/( x + 1)

A:

Q: Evaluate the limit - 1 lim x→1 r2 - 1 If the limit does not exist enter DNE. Limit =

A: Given: limx→1x3-1x2-1

Q: Evaluate the limit 6| lim x→6 x - 6. If the limit does not exist enter DNE. Limit =

A:

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

A: The value of the limit is 2. Take the first term as common term and simplify.

Q: Evaluate the limit  Limx->0 (ex-1-x)/x3

A:

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

A: Given limit is  We will evaluate this limit by direct substitution because exists at x=-2, that is…

Q: Find the limit. lim e^(-2x) x-->∞

A: To find the limit of e^(-2x) as x tends to infinity.Check whether the L Hopital’s rule applies.

Q: Let f(x)={−4x+3   x≠4               {3       x=4. What is f(4)? If f(4) does not exist, type: 99999…

A:

Q: 5) Find the indicated limit if it exist. 3- Vx + 7 а) lim x→2 2 - x x' +1 b) lim х>-1 х+1

A: (a).    We have to find the limit: limx→2 3-x+72-x

Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

A:

Q: Find the limit or show that the limit does not exist. lim→-0 4x2 + 3x + 2x x→-∞

A: See the details solution in below

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

A: We have to find limit

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

A: Given:

Q: lim (x²Vx* – 1 – x*)

A:

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

A:

Q: Find the limit. lim(v² + x = x) = lim( Vx2 + x – x

A:

Q: Calculate the limit limx→∞(1+6x)x.

A: limx→∞ (1+6x)x   = limx→∞ (x+6x2) = limx →∞ x + limx → ∞ 6x2 = ddx x + ddx 6x2 = ddxx + 6× ddx ×…