dy -from the function y= sint, x= cost as a parameter. da? Obtain

Q: I=Jx Incx) dx, where b is a constant with %3D bフ)

A: Intregation of product of two variables is given below

Q: dy Differentiate parametrically to find dx in terms of t: x = 4t?,y= 2t3

A:

Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: t^2 y^′′+aty^′+by=0, t>0 Define what type of equation is  mentioned above ?

A:

Q: (c) t? dy + 2ty = cost , y(T) = 0, t > 0. %3D dt

A:

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

A:

Q: Differentiate the function. y -Vetoo y%3D dy dx

A: Given :   y = 7√( ex + 6 )

Q: Given I 2 cost +35 and y = 6 sin' t dx %3D dt dy dt dy dx ||

A: Given: x=2cos t+35y=6sin2t Therefore, dxdt=ddt2cos t+35       =-2sin  tdydt=ddt6sin2t       =6(2sin…

Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

A:

Q: r(t) = (sint)i + (1+ cost)j + (4t²)k ind S r(t)dt :

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Q: Given the equation x In(y) = z Arctan(3*y). Assuming z as a function of variables a and dz find

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Q: Find dy/dx and dy/dx. x = e°, y = te-t dy %3D dx %3D For which values of t is the curve concave…

A: Given: x=ety=te-t Find dydx and d2ydx2 as shown below.

Q: Differentiate the function y = e0.4t. dy dt

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Q: Find dy/ dx and d2 y/dx2. For which values of t is the curve concave upward? x = et, y = te-t

A:

Q: ;(y+ 1) e*dx = (e* + 1)y dy, what is F = 1.F. J (-e*y - y)dy? %3D

A: Given: y+1exdx=ex+1ydy

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: express in the form y = f (x) by eliminating the parameter  x = cost, y = tan t

A:

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: Find  dy dx at the value of the parameter. x =    t,  y = 2t + 8,  t = 16

A: See attached file for a step by step explanation.

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

A:

Q: dy dy and Find dx dx2 x = e', y = te-t dy dx d?y dx2 For which values of t is the curve concave…

A: Apply ln on both sides is x=e^t

Q: "y=sin't+ tant, x=- In-cost)-e Snt, find the value ofy when t= 6/2 2-/2e 2 3/2 1 2+VZe V? 6. -Vle

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Q: dw at the given value of t: dt Evaluate w =x2+y x = cost +sint y = cost -sint %3D 2.

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Q: (d) y = V1+r² + sinhr (e) f(r) = sinh Vr +1 (f) y = In coth 3.r

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Q: f'(rr), where f(t) = sint cost

A: Given function is ft=sint cost To find: f'π Solution: Product rule of differentiation is:…

Q: dy Find for the given function. dx y = x° + sec æ – 1 dy Preview dx ||

A: y=x3+sec x -1  dY/dX=d(X3)/dX  +d(sec X)/dX  +d(-1)/dX           =3X2  +  sec X. tan X

Q: dy Find for the functions x = a(cost + tsint) , dx y = a(sint – tcost)

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Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

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Q: FIND dy AND d?y OF x= VI-t AMD y= t° -at dx

A: Given x=1-t , y=t3-3t

Q: Q2/ Find the extremals for : y" dx. JW) = | i) ii) Jy) = S,(v² +y² + 2ye*)dx.

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Q: d'y of the function x' +y' = 1 aluate y" or dx when x = 0.

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Q: Find the conditions such that the equation M (x, y) dx + N (x,y) dy = 0 mogeneous and exact.

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Q: Find- for the following function dx x=a(cost + t sint).y=a (sint-tcost)

A: y=a(sint-tcost), x=a(cost+tsint) To find dy/dx.

Q: Given the equation r In(y) = z Arctan(3*y). Assuming z as a function of variable dz and y, find

A: The given equation is xln(y)=ztan-13zy ........................................ (1)  Here z =…

Q: dy Given that y = find . dz'

A:

Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: Given z = 2 cost +35 and y= 9 sin t da dt dy dt dy dx %3D %3D %3D

A:

Q: Given x = 2 cost +33 and y=8 sin t |3D da dt dy dt dy dx

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Q: Determine the evolute of the cycloid x=t−sint,y=1−cost.

A: Given,

Q: dy Given the equation y In (x* +y +5) = 7, evaluate Assume that the equation implicitly defines y as…

A:

Q: w = xy +z xr = cost y = sint z=t a) Find at if

A: We have  w=xy+z x=cos(t) y=sin(t) z=t We have to find ∂w∂t

Q: dy h. Find dx 2-sint (a) y = dt (b) y= 2m +m+1dm 3+cost ー元 cost dt 12 +1 (c) y = [ (d) y= [ Ju…

A: As per guideline we have to solve only three subparts

Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

A:

Q: dy Find dx for the function y = ecotx

A: We want to find the derivative of the given function.    y=ecotx Here we apply chain rule of…

Q: dy d'y Find and at the given point without eliminating the parameter. dx dr? ㅎ + 4, y3D t +t, t = 2.…

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Q: dy when Find dx x(t) = te', y(t) = 2t + e'. %3D

A:

Q: Find for the following function x = a(cost +t sin t),y= a dy dx (sint – t cost)

A: Given problem is  :

Q: dy Given that y = x°e", find dx dy dx

A: In this question, we need to find the derivative of y = x9ex

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.