Evaluate 4x' – 1 lim 3x +2 sin (E).

Q: Investigate lim sin

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Q: Evaluate limx-->0 (sin 2x sin 9x)/(x^2) Without using L'Hospital's rule.

A: The given function is limx-->0 (sin 2x sin 9x)/(x^2)Use the expansion for sin x to simplify (sin…

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

A: The given limit is,

Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

Q: lim at e -

A: Find the limit when x tends to 0

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

A: On direct substitution we get limx→0 sin xx=sin 00=00

Q: What is the limit of (sinx)/x if x approaches to 0?

A: Given: A function limx→0sin xx and x approaches to 0. Since sin xx is an intermediate form of type…

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

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Q: 10) lim TT X-- sinx-cosx - TT X- 4

A:

Q: ,3x lim x→0 CO cosh(Зa)

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

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: Find the limit of * sin(6x) limx→0 sin(2x)

A: Given problem is :

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

A: The given funtion is (sin^2(2x))/2x for the limit x tends to 0.

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: Find the limit of tan(4x)/sin(6x) as x approaches zero.

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

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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: In(sin 4x) \ In(sin 8x) lim x → 0

A: We have to evaluate the limitlimx→0ln(sin4x)ln(sin8x)

Q: 3. Find the limit. tan(5x) 0 sin(3x) sin(6x) (2) lim x04x-5x (1) lim

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Q: Evaluate using substitution. lim tan -1 (ex)x→ 0

A: to evaluate the limit

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

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Q: Show that limx→0(√x) cos(1/2x) = 0.Show your work.

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Q: sin x 34. lim 1 - x o0-r

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Q: Find the limits. sinh 3x 1) lim arctan 2x

A: We have to find limit

Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

Q: se L'Hopitals's rule to find lim xIn(e* – 1).

A: Given query is to find the limit of the expression.

Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

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

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

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Q: Evaluate exactly lim (1 + sinx)²cotx x→0

A: This question is indeterminate form of 1infinity and solved using L Hospital rule.

Q: Evaluate using substitution.

A: We have to calculate the following limit L:

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

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

A: This question is based on Limits.

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: Calculate lim-x+sin x x0 -1+ cos x

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 x→0 for sin(4x)/3x

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Q: lim sin (xt3) dt X 5

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Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

Q: lim (sec 2x) cot? 3x x→0

A: Limit that are end up in indeterminate form which are 00, ∞∞, ∞-∞, 00, 1∞, ∞0, 0·∞, we use…

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: Evaluate limt--&gt;0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt--&gt;0(sin 3t)/(sin 6t).

Q: lim as x→0 of sin(x4 )/x

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Q: sin(3x – 3) lim x² – 1

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Q: 4. lim In(cosx) 2

A: Given limit, limx→π2-ln(cos x)

Q: Evaluate L = limx→∞  (X2 sin(1/x)

A: We have Let's first try to use direct substitution   We can use the L'Hospital rule if our limit…

Q: Find lim Sin 3x (1- Cosx) メーや。 メ*s X Sinzx cosx

A:

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…