Use the definiton of the derivative to find lim x--->0 Ln(1+×)/×

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: 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: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: g(x) = In tanh-1 x

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Q: Use the definition of derivative to prove that In(1 + x) lim 1

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

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Q: In evaluating 5 dx , is same as evaluating_lim_(in(f(x))). Determine the value of f(x) if x=4.6. -

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Q: tan(2r) lim 3r+ sin(x)

A: As we know that: limx→afxgx=limx→afxlimx→agx And we know that the identities of limit.…

Q: Find the limit of the equation.

A: Limit x-> pi/4 means x is approaching pi/4 .Plug x=pi/4 in the expression.

Q: Find the one-sided limit (if it exists).

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Q: Decide if you can evaluate the following function using substitution. If so, state why and find the…

A: Given,  limx→π2sin x+x2

Q: Find the derivative y=arctan(square root 1+x/1-x)

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Q: 13. f(x) = e* In x

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Q: Use the difference quotient f' (x) = lim f(x + h) – f(x) to find h→0 ん derivative of the function…

A: To find the derivative of the given function by using difference quotient formula.

Q: dy Discuss the relationship between the derivative and (Lim) with drawing if it is dx

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Q: Find the slope of the tangent line to the graph of the given function using the limit definition of…

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Q: 4. lim logz(x? + 2х + 1) X→3

A: Given, limx→3log2x2+2x+1   The objective is to evaluate the limit.

Q: Evaluate the limit sin 9x lim x →0 sin 3x

A: We can solve the problems by finding the value of the function at  the given limit.

Q: Find anti-derivative if possible of: sqrt(tan(x))  dx

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Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch x 8118

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Q: Find the limits in Exercis

A: To evaluate: limx→0sin5xsin4x Solution: Given,limx→0sin5xsin4x On simplifying further we get:…

Q: In(tanhx)

A: As we know that; The chain rule: fgx'=f'gx·g'x And ddxtanhx=sech2x Given: fx=lntanhx

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

A: We have to find limit limx→∞logx+1log2x We know that logab=logbloga So, the given limit expression…

Q: Using the fact that lim = 1, show by formal definition of a derivative:

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Q: Q2/ Discuss the relationship between the derivative and (Lim) with drawing if it is dx required ?

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Q: State the definition of the derivative of a function f. Use the definition of the derivative to…

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Q: (a)x =-5t-3

A: Simply use the power low of derivative and simplify.

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: se Ľ' Horpitals Rule to find X>0 lim e2x_I SInX

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

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Q: Evaluate the limit lim of 02 04 00 of tan(+)-tan() by recognizing it as a derivative of some…

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Q: Please provide on how you did it step  by step. Use one of the two limit definitions of the…

A: The given function is  f(x) = 7/x To find the derivative of the function by using definition at x =…

Q: Find the limit. sin(x – 3) lim х>3 x* + 5х — 24

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Q: Find the limit. sin(x°) lim

A: to find limx→0sinx9x

Q: Find the derivative. Simplify where possible. y = x tanh-lx + In /1 – x²

A: We have to find

Q: f'(x) at x if f(x) = csc³(x).

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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: Find the derivative. Simplify where possible. |(a) y = ln(coshx)

A: Find the derivatives

Q: Approximate the value of et – 1 lim x→0 2x2 + X by substituting in 3 different values of x that get…

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Q: Find the value of lim tanx

A: As per our guidelines we only solve question number 1 . If you want the solution of other parts…

Q: - lim SinTX メー→ メ ー」

A: We need to evaluate limx→ 1sinπxx-1.

Q: lim x→0 4-Vx+16

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Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

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: Match the given limit with a derivative. Then find the limit by computing the derivative. lim 49 h-7…

A: Derivative by definition formula is

Q: Use the definition of the derivative to compute the derivative of the function f(x) = 1 – 6x at an…

A: We plug the given expression of f(x) in the limit. This is the difference quotient.

Q: We determined that l'Hospital's rule applies to the limit  lim x→5   x2 − 10x + 25 x2 − 5x

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Q: Calculate the derivative of f(x) = x² – 3 at a using the (limit) definition of derivatives, by…

A: Given function is We will calculate f'(a) by using definition of derivatives as follows.

Q: Find the derivative. Simplify where possible. g(x) =   cosh (   ln x )

A: Given: gx=coshlnx

Q: By interpreting the function as a derivative, find the limit as x goes to pi over two when (sinx -…

A: From the definition of the derivative at x=a. f'a=limx→afx-fax-a Given:…

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: