. Explain the flaw in the following calculation: limx→0 x 2 sin(1/x) = (limx→0 x 2 ) · (limx→0 sin(1/x)) = 0 · (limx→0 sin(1/x)) = 0.

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: What is lim Sináx, cosx А. 0 В. 6 С. 1 D. Ø (DNE) Ø (DNE)

A:

Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Plot the function and use the graph to estimate the value. lim 2x − cos x/xx→0

A: Given:

Q: why is the limit as x approaches 0 equal to 1/5 in the equation: ((sinx)/(5x))

A: The given limit is,

Q: Evaluate the following limits. x + sin(x) + 2vT x + sin(x) V1+x – 1 – 5 a) lim 2 b) lim r2

A: Given: a  limx→∞x+sinx+2xx+sinxb limx→01+x-1-x2x2

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

A: The L’Hospitals rule is used to obtain limits of a function when it occurs in the indeterminate form…

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

A:

Q: LEvaluate each of the following limits without using "L'Hôpital's Rule": 5-|x-4x2| 82x3+x2-8…

A: Indeterminate forms: The limit of A(x)B(x) when x→a when limit of both function exist and if both…

Q: Find the limit of the trigonometric function.

A: Given: limx→π2sin x To Find: The limit of the given trigonometric function

Q: Lim 1 1. Sin?s

A: Since , we have an indeterminate form of type 00 , we can apply the L'Hospital's rule.

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

Q: sin 3x 1. lim x0 tan 4x 1-cos 2x 2. lim X-0 sin 2x x2-x+ 3. lim 5 X-00

A:

Q: 2 sinlbx) +1-cosX lim

A: Given,           limx→02sin4x+1-cosxx

Q: sec x -tan x lim -X 2 X- 2 .2 x²+sin 3x lim X→0 2x+tan 2x

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 8r + 5tant Find lim t>0 sint

A:

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

A:

Q: plot the function and use the graph to estimate the value of the limit.

A: Consider the following limit:…

Q: Evaluate using substitution.

A:

Q: Find the limits

A:

Q: ■ Find the limit.

A: Here limx→∞sin2xx2=limx→∞sinx2x2.

Q: sin x lim bx = ? Use L'Hospital's Rule

A:

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: sin(6t) lim +0 sin(11t)

A: The limit of a function (expression ) is a value of that function (expression ) approaches as the…

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: Evaluate cot x – cos x lim z¬7/2 (T – 2æ)°

A:

Q: Calculate the following limits. x² – sin²2x lim X→0 x2

A:

Q: Find lim In(sin x) cos x by using L' Hospital's rule

A: Let a limit in the form limx→af(x)g(x), where f(a)=g(a)=0, i.e. 00 form, then use L'hopital rule…

Q: Express the following as an algebraic function of x. sin(arctan(2x) + arccos(2x))

A: Question is solved.

Q: Evaluate limt-->0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: Find the limit tan (x) cos(3r) lim sin (2x)

A: Topic:- limits

Q: - Find the Lim;t: O Lim Sinx メー0 12ナメ3 E. 4) Lm sint2 sino lim 下-日

A:

Q: How do you solve the limit of this graph?

A: x->-1^- means x is slightly less than -1.

Q: Evaluate the following limits. x + sin(x) +2Vã x + sin(x) a) lim

A: NOTE***As per bartleby guidelines for more than one question, only first to be answered send other…

Q: 1) Answer the following: 1. Find: lim-5-25 x-5 2. Find x2 + y? = 9xy dx 3. Find y': y = 5 sin3x

A:

Q: Find the value of : sin3x lim x→0 2x

A: This question is based on Limits.

Q: Lim 1 Sin?x

A: Calculate : limx→01sin2x-1x2

Q: Express the following as an algebraic function of x. sin(arctan(2x) – arccos(2x))

A:

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: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

A:

Q: Find the arc length of f(x) = In(sin(x)) for - 10 8

A:

Q: Why is it not possible to evaluate by direct substitution?

A: Given: limx→0sin xx To check: Why it not possible to evaluate by direct substitution.

Q: lim sin (xt3) dt X 5

A:

Q: Calculate the following limits. cos x 1) lim (tan x)cos* x² – sin?2x 2) lim x→0 x2

A:

Q: 7x( cos (4x) – 1) Use l'Hôpital's Rule to evaluate lim sin (5x) – 5x

A:

Q: Find Lim o'sin to Sin 02

A: We use the properties of limit and L'Hopital's Rule to find the limit in the given question.

Q: Find the value of limx→0 sin(sin x)/x

A: L'Hospital Rule: According to this rule limit of the intermediate form 00  or  ∞∞ can be solved by…

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx