Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

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Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - -x(²+y²). sec̟. tan?…

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Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

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

A: Find the limit

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)<0 and f(b)<0.…

Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: Find the differential dy of the given function. y = 3x − sin2x

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Q: Let y tan(2x + 2). || Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: We have to find the differential dy

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Let y=tan(2x+6) Find the differential dy when x=1 and dx=0.2 Find the differential dy when x=1 and…

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Q: Use the appropriate form of the chain rule to find the derivatives. 7x2 + 7y? + z²; x = psin ø cos…

A: This question is based on Partial derivatives.

Q: Let y tan(4x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when x…

A: Given : y = tan(4x + 6)   To find the differential dy when x = 5 and dx = 0.2 Also to find the…

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: let f(x,y)= z-sin(xy),x= t, y= lnt, z=e^t-1. find derivative of f directly and by using chain rule…

A: Plug the given expressions of x,y, and z. Then differentiate directly. And plug t=1

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: If Z = Jxy +y, x= cos 0 , y= sin 0 when 0 dz By using chain rule find de

A: Chain rule for one independent variable- Suppose that x = g(t) and y = h(t) are differentiable…

Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: S2ta J 2tan x In (cos x) dx=

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Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

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Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Find the antiderivative of f(x)=cos(3x)

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Q: Let y = tan(4x + 7). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and da Find the differential dy when x = 3…

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Q: Let y = tan(2x +5). Find the differential dy when x 3 and dr = 0.1 Find the differential dy when z =…

A: Given that y=tan(2x+5) find the differential dy when x=3 and dx=0.1 find the differential dy when…

Q: Find the differential dy of the given function.    y = x tan x

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Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: Let y = tan (3x + 3). Find the differential dy when x = 3 and dx = 0.4 Find the differential dy when…

A: Given is the function y=tan(3x+3) We need to find the differential dy when x=3 and dx=0.4. and…

Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: Let y = tan(5x + 5). Find the differential dy when a = 2 and dx 0.3 Find the differential dy when x…

A: Given, y= tan(5x+5) Therefore, dy/dx = sec²(5x+5) .d(5x+5)/dx dy/dx = sec²(5x+5)*5 dy= 5sec²(5x+5)dx

Q: Let y tan(4x + 8). Find the differential dy when x 5 and dx = 0.2 Find the differential dy when x =…

A: Topic = Derivative As per guidelines , At a time only one question can be answered.   use formulalet…

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

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Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

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Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: find the differential dy of the function y=x2sin(8x)

A: Find the differential dy of the function y = x2 sin(8x) as follows.

Q: Let y = tan(3x + 4). Find the differential dy when x = 4 and dx = 0.4 Find the differential dy when…

A: We know that, ddxtanx=sec2x We have,  y=tan3x+4 On calculating derivative with respect to x, we get…

Q: Let y=tan(3x+3). Find the differential dy when x=5 and dx=0.3  Find the differential dy when x=5 and…

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Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

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Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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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.