cos x D. Explain why we cannot apply L'Hôspital's rule to evaluate lim x-0

Q: Why does the lim as x approaches 0 of sin(x)/x = 1. We haven't learned derivatives so I wasn't sure…

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

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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: How many times must l'hôpital's rule be applied to evaluate ex - e-X – 2x lim X + 0 X- sinx

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Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Use the Simpson's Rule with four strips to estimate the value of: L(-x In x)dx. Note that lim,x→0 x…

A: Using simpsons 1/3 rule we can solve this problem

Q: Why can't L'Hopitals Rule be applied to evaluate x - cos x lim x→+00 x + sin x

A: We have to explain about the given information

Q: True or false: lim(sin) as x goes to infinity exists.

A: Given, limx→∞sinx Find in the following that this limit is exist or not.

Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: x-Arcsinx lim x3 1 lim X0 sin?x 1 x2

A: (a). We have to find:   limx→0 x-sin-1(x)x3

Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: 3x tan(2x Use L'Hopital's rule to evaluate lim sin(4x)

A: Using l hospital rule we have

Q: 1-cosx 16. lim X-0 3x sin x

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Q: 4. Use L'Hopital's rule to evaluate lim(1 – 2 sinh(r))ach(=).

A: 4) To evaluate: limx→0(1-2sinh(x))csch(x)  which is in 1∞ form.

Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

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Q: tan(1 – x) 2 limx→1 2x +x – 3

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Q: If x sinx < 1 2 - 2 cos x hold for all values of x close to zero. Find limx¬0 xsinx ? 2-2cosx

A: 1-x26&lt;xsinx2-2cosx&lt;1 holds for all values of x close to zero. Now, limx→01-x26=1-0=1 &amp;…

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: Find the limits

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Q: In(sin 4x) \ In(sin 8x) lim x → 0

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

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

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

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Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

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

A: It is given that,limθ→0θ-sinθcosθtanθ-θ We have to find the limits using L'Hopital rule.…

Q: Prove that lim sin( nx) + n dx= In 2 . (n+) Explain your answer carefully

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Q: Plot the function and use the graph to estimate the value. lim sin 5θ/sin 2θθ→0

A: Using a graphing calculator we graph the function

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

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

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

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

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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: 2.) lim cot x- sin 2x cotx-1 3.) lim x0 cotx+1

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Q: tan(4x) lim sin x [Hint: Use the fact that lim,→0 = 1.]

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Q: If sinh(x) = 35 =, find the values of the other hyperbolic functions at x. %3D cosh(x) tanh(x)…

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Q: how do you express lim,,→ Li=1 Σ! as п 1+ definite integral

A: We know that

Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: Use the relation lim sin 0 = 1 to determine the limit. 0→0 tan 3x lim sin 8x

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Q: lim sin (xt3) dt X 5

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

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x→0+ 1 1 (b)…

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Q: cos(x) lim COS 21

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

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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: 3. Show that the function | sin(2.x)| is not differentiable at r = 0 but the function | sin(2x)|1+T…

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Q: -) Compute lim_(sec r – tan x).

A: