What is the sign of the coefficient multiplying x' if f is a polynomial of degree 7 such that lim f(x) = 00? X -00

Q: Evaluate lim f(x) where f(x) = x +2 cosx +1 e-4 for x20

A: Use the existence of limit definition

Q: Find the limit. 15) lim V3 + cos2 x A) 2 16) lim (3 sin x - 1)

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

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Q: Determine the limit: 12 x+ 1 tan(2 x) lim 3 sin(3 x) X- 0

A: Given limit: limx→012x+1tan2x3sin3x

Q: tan 3h 3. Estimate the value of lim,0- by creating a table of function values for h h = 0.01,0.001,…

A: We need to substitute these values of h in function f(h) to evaluate limit

Q: Evaluate: 1- cos(x) lim 3x2 X+ 0 Express your answer in 4 decimal places.

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Q: Calculate the difference quotient for f(x) = 5 - x^2 at a = 4 f(x) - f(4) / x - 4 = ?   lim  f(x)…

A: Given function is f(x)=5-x2f(4)=5-42=5-16=-11 Now, difference quotient for f(x) is…

Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: Find the limit of the equation.

A: Limit x-> pi/4 means x is approaching pi/4 .Plug x=pi/4 in the expression.

Q: lim as x-->0  of (x+1-cosx)/x

A: The given limit of the function:

Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: Find the limit. sin 5x lim X0 3x

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

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Q: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

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Q: Show that lim [x2 sin (1/x)] = 0.

A: Given: limx→0x2sin1x

Q: Find lim f(x) and determine if continuous at x =2 エ→2

A: We have to check

Q: Prove that lim x->0+ √ x [1 + sin2 (2 π/x)] =0

A: Given: limx→0+x1+sin2 2πx By using the property of limit, the limit of a product is the product of a…

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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Q: Show that lim sin( does x→0 x2 .not exist

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Q: Find the limits limx→0+x-1/ln x

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Q: Evaluate limx-->0 (x^2)/(sin^2(7x)) Without using L'Hospital's rule.

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Find the limits in Exercise

A: To find the limit  limθ → π6 sin θ - 12θ - π6

Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

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Q: Calculate the limit for the function f(x) = 33 – 11x and interval [2, 6]. Verify your answer by…

A: Given that: f(x)=33-11x in [2, 6]

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

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Q: 1 lim sinx x2 x→0

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: sin² x lim 0-x X

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

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: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

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Q: (sin 2x)* - 4x →0+ x -

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Q: Find the limits limx→0(ex + x)1/x

A: Consider the given limit as limx→0ex+xx

Q: Q3: Choose A or B (one only) fx2 +2x x-6x if xs-2 if x>-2 A) Check the continuity of the function…

A: Since we have to choose only one part of the given question, therefore we choose part (A). To check…

Q: Find the limits lim x→1- sin-1x

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Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

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Q: Lim (Ln x) L'Haspital Hos

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Q: Find the limit. lim x→4  sin(x − 4) x2 + 5x − 36

A: To Determine: find the limit of  limx→4sin(x-4)x2+5x-36 Given: welimx→4sin(x-4)x2+5x-36 Explanation:…

Q: Find lim 2x sin using the Squeeze theorem. x-0

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Q: Find the limit limx→0ln(1+4x)sin3x.

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Q: Show that lim x sin l/x = 0.                   x→ 0

A: It is known that the absolute value of sine function is not greater than 1, then  -x≤xsin1x≤x

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: Find the limits: (1) lim (tan x)* X-0+ (2) lim (sin x)* (3) lim (ex + x)² X-0+ X-00

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Q: Evaluate lim→» V3 - cos x

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Q: Determine whether f(x) approaches ∞ or – ∞ as x approaches -2 from the left and from the right. TX =…

A: Given figure To evaluate

Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

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Q: lim as x→0 of sin(x4 )/x

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

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and…

Q: Find the limits using any appropriate method. ex-e-x-2x 4.4 #40 lim x-0 x-sinx

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Q: Find the limits limx→0+sin x . ln x

A: The given limit is: limx→0+sinx·lnx  Consider "h" is a too small positive real number,  Then,…