Answer all the following 1- Find y" for y = x².tan-1x -1+cos2x 2- Find lim (by using L'hopital's rule) 7x 3- Find y' for y = x².e*

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: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Define ro = 0 and xn+1 = In chis to Newton's method. tan(r,)-1 sec2(z,) What is lim, Pn in this…

A: In the given question we have to find the limit of the sequence xn as n→∞ where the recurrence…

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

A: Find the limit

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

A: Using formula.

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: The area under the entire curve is given by 15 dx. We have 00 15x-3 dx lim 15x-3 dx - lim - 00 lim…

A: The area under the entire curve is given by  ∫1x15x3dx

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

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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: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: Find the slope of the tangent line to the curve: 3.) Ħan0 at 0=n/4 4.) sin20 at 0=x/3 5.) rcos20 at…

A: Use the formula for the slope in case of polar coordinate.

Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: 1+3x – cosI 2.) lim tan x

A: limx->01+3x-cosxtanx When we plug in 0 for x then we get…

Q: sin 3x 1. lim x0 tan 4x 1-cos 2x 2. lim X-0 sin 2x x2-x+ 3. lim 5 X-00

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Q: 2 sinlbx) +1-cosX lim

A: Given,           limx→02sin4x+1-cosxx

Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: tan(1 – x) 2 limx→1 2x +x – 3

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Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

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Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

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Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

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Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

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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: 4. The given equation sinh(xyz) = x+ y + 3z implicitly defines a differen- dz Find ax tiable z as a…

A: Differentiate of sinh(x) =cosh(x)

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

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Q: Q3: Find lim,- (2 – sin –) إجابتك :Q4 For (3x³ – 5x) V2x+1 find dy/dx at x=0 إجابتك

A: Explanation of the solution is given below...

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: Find the indefinite integral. ∫4 arccos x dx

A: To evaluate the integral: ∫4cos-1x dx Integration by parts states that: ddxuv=v·ddxu-∫ddxv∫udxdx…

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

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Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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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: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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

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Q: 5. Find the slope of the graph of cos(x + y) = 2x at the point ( 0, n/2 ). Hint: Differentiate…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 7x( cos (4x) – 1) Use l'Hôpital's Rule to evaluate lim sin (5x) – 5x

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Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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Q: Given the function y = 6 cos(3x + 1) The second derivative y" %3D Select one: 18 sin (3x + 1) -18…

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Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

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…