d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are used.

Q: Compute the following derivative: tan e dr 30 – cos 0

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Q: Find the limit of the trigonometric function.

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Q: Prove that  d/dx[cot(x)]= -csc^2(x)

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Q: d (arccot(x)) -1 Be sure to provide a written justification for 5. Prove your work. dx 1+ x2

A: Gg

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

A:

Q: Find the limit of sin Ø/Ø as approaches 0°. * 00 1 -1 ООО

A: Using formula.

Q: Determine whether the statement (d/dx) [arctan(tan x)] = 1 for all x in the domain. is true or…

A:

Q: Complete the following argument that sinx#x for any x in the interval (0,1): • For any x in (0, 1),…

A: 1) the mean value theorem . 2) c . 3) is greater than . 4) is greater than .

Q: Prove the following derivative statement. Include supporting mathematical statements within a…

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Q: d Q 3. Prove that tanx dx sec?x. =

A:

Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Li sin sin dx = where m n 04: Prove that: %3D where m = n

A: Topic:- integration

Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: Find the limit of the trigonometric function.

A: The given expression is limx→06-6cosx3

Q: Integrate the following. 3. f sec?x dx tanx

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Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: What is the limit of sin when x approaches 0? Select one: O a. 1 O b. 0 O c. Does not exist

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Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Use symmetry to evaluate the followingintegrals.

A: Given:∫-11 1-x dxIf f is an odd function f-x=-fx∫-aa fx dx=0If f is an even function f-x=fx∫-aafx…

Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

A: Sine function and it's continuity at 0

Q: Use linear approximations to estimate the following. 1. sin 9/4

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Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

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

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Q: if Pen) = Sinh(nw) find F(Z)=?

A: There is an exponential representation of sinhx. Whenever we analyse various properties of sinhx, we…

Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

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Q: Differentiate the following finction f(x)=sin(3 ln(x))

A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

Q: Use the Reduction Formula to evaluate the following (a) f sin“ x dx (b) S tan x sec4 x dx

A: (a) The reduction formula for ∫sinmxdx is given as the following.…

Q: 2 If s Sinants COs ant 3 an= ০ । A. limitdoes not exist 2.

A: Series and sequences

Q: If ƒ is continuous everywhere and 1| f(x) dx = 6, find | sec? 2x · f(tan 2r) dr.

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Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

Q: Find the limit of the trigonometric function.

A: The given expression is limx→0cosx-sinx-12x

Q: Ex O Finel the dimit of the FoMowing gi. Lim ナスSinx メー>。 Y Cos 2K tan? x Solution:

A: Solution:Givenlimx→01+x sin x-cos 2xtan2 x2Formulalimx→0 sin xx=1limx→0 tan xx=1cos 2x=1-2sin2x

Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: 2. f(x) = sin x [0,21]

A:

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: Let F(x) = / sin(5t2) dt

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

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Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

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Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: 4. Use definition (not tables) of L{f(t)}= [ e"f(t)dt to find L{sin(2t)} .

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Q: d Prove, through the limit process, that (cos x) = - sin x. dx

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Q: A pdf is given by 2 cos (x 3 ").0<x< f(x) = 3 Show that this is a valid pdf and then find P(X<1).

A: Topic:- probability

Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.