Lind Lim Sin'(Ox) sin (sx) X-o

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: Find y′ if y = tanh−1(sinh x2).

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Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: (5x) S sin(x) tan(x) .........

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Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

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 do the limits limh→0((sin h)/h) and limh→0((cos h - 1)/h) have to do with the derivatives of…

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Q: Find the derivative

A: To compute the derivative of ln|cscx|

Q: Limit as x approaches 0 1-cos(x)/sin(x)

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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: te dt lim 0 x-0 sin x =?

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

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Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

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

A: See the attachment

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

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Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

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

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Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Evaluate S sinh x cosh x dx by letting u=cosh x

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Q: lim 3 2y ソ→o ソーSiny -sin.

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

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

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

Q: Find y' by direct differentiation (with respect to x). y = 10etan(x) and y = (x3 + 4) sin(x)

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Q: Obtain the derivative formulas for csch x, sech x, and coth x from the derivative formulas for sinh…

A: Given functions are sinhx,coshx,tanhx.

Q: x-sinx 1. lim X-0 x-tanx

A: Given function is limx→0x-sinxx-tanx

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

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

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Q: Show that d /dx  arctan ( tanh x ) = sech 2x

A: We have to show that ddx(tan-1tanhx)=sech2x

Q: Find the derivative of y=arcsec x at x=√2.

A: Given:

Q: Find the derivative. Simplify where possible. h(x)  =In(Cosh  x)

A: Given: h(x)=lncosh x To find: we have to find the derivative of h(x)

Q: Y=メ* Sinx+x (0) メ +X CO) メア

A: we also to derivative

Q: 2/ Pind the Pirst derivative X. tan X. (3-2x ). 5x

A: Given equation is: y=x5.tan-1x3-2x.x3 To find the first derivative.

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

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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: In(cos(x)) Find the derivative of cos(In(x))

A: Derivative using quotient rule (f/g)'=(gf'-fg')/g2

Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

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

A: This question is based on Limits.

Q: Find limit   without using derivative

A: Given,

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

A: We know that

Q: The L'Hopital rule and The derivative of the exponential function. lim (ex + x³)*:

A: Use l hospital rule

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

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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: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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

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Q: Se Sin (3x) dx by Improper htegrations.

A: use improper integral

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.