Question 5 Transform the function lim x +3-x²) into an equivalent quotients to enable you to apply L'hopital's rule.

Q: compute lim as x goes to pi/2 from the right of (x-pi/2)tan(x)

A: Given f(x)=x-π2 tanx To find limx→π2+f(x)=limx→π2+x-π2 tanx

Q: Find the limit of the trigonometric function.

A:

Q: QUESTION 10 Compute the limits. Justify your answer. (You will receive no credit without showing…

A: The limit of given function is computed directly by using some results

Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

A:

Q: EXAMPLE 9 Using Substitution Find lim sin (1/x).

A:

Q: Find the limit of the trigonometric function. lim sin8) X → 3

A:

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: 6. lim (sinx)*

A:

Q: QUESTION 6 | 16-ydy can be eliminated by applying lim t+ -0 6-ydy The infinity in the O True O False

A:

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: Find the limit of the trigonometric function. lim cos X-9

A: Limit of a function can be found at x→a just by evaluating value of the function at x=a, provided it…

Q: 1. Determine where f(x) = arcsin (x² – 2x) is increasing. %3D

A:

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

A: Let y=tan(3h)h Then we make tables for the given values. h y 0.01 3.00090032412 0.001…

Q: Prove that lim |x|sin(1/x) = 0.

A: We need to prove that limit of given function is zero.

Q: Find the limit of the trigonometric function. lim 9 sin(x)

A:

Q: 2. Find limits numerically. Use at least 3 relevant x-values for each. sin(4x) sin(4x) (a) lim x→0-…

A: Explained below

Q: Question 19 Let f(z) = 3x + 8x 7. According to the definition, f'(x) = lim %3D (Enter the expression…

A:

Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: Find the limit of the trigonometric function.

A: limx→3tanπx4

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

A: According to question,Given limit,limx→0 1- cos x3x2

Q: b- lim [In(cos(x))]= x->0

A: Given that:limx→0[ln(cosx)]x

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

A: Given: limx→0x2sin1x

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

A:

Q: Зх — 1 x + 5 - Let f (x) Find f' (x). First set up the limits and simplify the first one. Using…

A: Consider the given function  fx=3x-1x+5

Q: Question 1. Evaluate the following limits and use L`Hopital`s rule if applicable (10 pts) x - sin x…

A:

Q: I. Apply the different techniques in evaluating the each item, you have to show your work at each…

A:

Q: (1) lim,o In (sec x) 3x (2) lim, (tan x)*

A:

Q: 1. Find the limī lim In(sin x) X→π-

A:

Q: tan Ø 10) lim Ø→0 sin2Ø

A:

Q: Find the limit of the trigonometric function.

A: To find: The limit limx→5π3cos x. Formula used: Trigonometric reduction Formula: cos 2π-α=cos α…

Q: Clearly explain why lim (sin-(t) is equal to 1 and not zero. t+0+

A:

Q: Show that lim |x|cos 0.

A: We have to prove that limx→0xcos1x4=0. Use property, if limx→a−fx=limx→a+fx=L then limx→afx=L. First…

Q: lim (In(x))* ?

A:

Q: (sin 2x)* - 4x →0+ x -

A:

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

A:

Q: Question 5- Evaluate the limit. Vx-1 lim Question 6 - Find the equation of the tangent line to y = -…

A:

Q: Find lim (e-2x cos x) (Hint: Squeeze Theor

A:

Q: Question 3 arctan(3x) lim ( Select) X--0 ex -1 1/x lim x--0+ In x ( Select)

A: to find:- limit.

Q: sin@ - Ф 8) lim Ø→0

A:

Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

A: Solution. :

Q: Example 8 Prove that sin x lim = 0. X00

A: We have given a question they're asking for how do we evaluate limit for sine x over x when x…

Q: Question 3: Show that 5xy² lim (x,y) (0,0) x² + y² does not exist.

A: To show that- lim(x,y)→(0,0)5xy2x2+y4 does not exist. Here we will find limit along the curve x=y2m…

Q: Show that lim x|cos )= = 0.

A:

Q: Evaluate lim→» V3 - cos x

A:

Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

A:

Q: lim as x→0 of sin(x4 )/x

A:

Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)