Choose the correct answer for the following limit sin(x) – tan-"(x) lim x→0 3x3 (A) 3 (B) -1 15 (C) (D) (E) 6. (F) -1

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: Evaluate the limit: sin(2x) cos(5x) lim

A: Given,           limx→0sin2xcos5xx

Q: Find the limit. sin (3y) lim 4y

A:

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

A:

Q: Find the limit using lim sinx 1. X-0 x 5) lim sin(sin x) x0 sin x A) -1 B) 1 C) does not exist D) 0

A:

Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

A:

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

A:

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

A:

Q: Evaluate the limit sin x/x as x approaches 0 when x = -1

A: We have to evaluate

Q: Find Lim as x approaches 0 of the function cos(4x-1)/2x

A: Given: limx→0cos4x-12x To find:  The limit limx→0cos4x-12x

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: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: find the limit. limit as x approaches 0 sin23x/x2

A: Apply the limits and find the in-determinate form.

Q: evauluate the limit lim x→0 (sin2 (3x))/ x2

A:

Q: Use l'Hôpital's Rule to evaluate the limit. cos (3x)-1 lim x² 2.

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: Find the limit of the trigonometric function .

A: The given limit limx→0cosx-sinx-12x can be evaluated as, limx→0cosx-sinx-12x=cos0-sin0-12×0…

Q: (d) Determine the following limit using u-substitution method: sin(t - 1) lim -1t2 +t – 2

A:

Q: What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

A: we have find the value of limx→0ex-e-xsin x

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: Find the limits lim x→ -1+ cos-1x

A: We find the limit by substitution

Q: 1. Find the limit of the following functions: x2/3+x-1 lim e x2/3 + cos² x 1- cosx lim- -+0 sin2x

A:

Q: Determine the value of the following limit. sinh(x) = x lim - x3

A: Given that limx->0 sinhx-xx3

Q: Evaluate the limitlimx→0+x sin(x) + x^2/ x^2

A:

Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: Determine the following limits analytically.

A: limx→0  3tanx - 8x3x + sin2xlimit = ?

Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

A:

Q: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: Find the limits in Exercise

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

Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ? B) Find the limits by…

A:

Q: Find the limit.  limit as x approaches 0 sin3x/x

A: Apply the limits and find the in-determinant form.

Q: sec lim x→1+ Vx7-1

A:

Q: Find the two limits: sin 2x lim r-T/2 COS x

A:

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x A) 3 B) 0 C) D) Does not exist 4/5 -/2

A:

Q: cosx * sin? (3x) 2 2. lim x→0 x2

A:

Q: Find the value of the limit: lim x→0* sinx+ tan x

A: Given query is to find the value of the indicated limit

Q: According to the alternate form of the definition of the derivative, to compute f′(0), we need to…

A:

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A:

Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: Find the limit of tan^-1(e^(x^2)+x^2+1/x) as x approaches negative infinity

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

A:

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

A:

Q: Find the following limit limx→0 (1/sin x − 1/x)

A: limx→01sinx-1x=limx→0x-sinxx·sinx=0-sin00×sin0=00

Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find the limit as x approaches zero of f(x)=tan(x)/x

A:

Q: 2. Calculate the following limits. sin 3x a) lim х-0 2х(х-3) V4+h-2 b) lim h→0 h 5х-4 c) lim X→∞…

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

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Q: Calculate the limiting value for 1 cos(x*) – 1+5x³ lim x→0 х16

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Q: What is the limit as x approaches 0 of 2x/sin(x)

A:

Q: Compute the following limits if they exist. sec r - 1 (a) lim I0- r3 x – sin x (b) lim I0 x - tanr 2…

A: We are entitled to solve 3 subparts of first question so, I am providing you the solution of the…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: