Hw)if J-0-Gso and X=e+Case Show thnt Sece+tan 0

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

A:

Q: Given that Sinh Ys 2. fnd sech x, eanh y with draw atiangle

A:

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

A:

Q: The prolate cycloid given by x = 2t − π sin t and y = 2 − π cos t crosses itself at the point (0,…

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Q: 3. Find the length of the curve y = In (cos x), 0 <x <

A: we have to find length of the curve

Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

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: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

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

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

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

A:

Q: 8. Find the arc length of y3 + y = x² + 6x on the interval [-5, –1].

A: Given equation of the curve is y3+y=x2+6x                     (i) To find the arc length in the…

Q: 2. Find the arc length of (x+5 y= over the closed interval [-1,4] .

A: Given curve is

Q: 28. Show that the graphs of y = tan x and y = cot x have nohorizontal tangents.

A: A horizontal tangent line is a mathematical feature on a graph located where a functions' s…

Q: 1- cos(Vr² + y?) lim (x,y)→(0,0) • (a) Va2 + y?

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Q: Find in terms of x and y if arctan(r + x²y) = ry

A: Given that         arctan(x+x2y) = xy We have to find dy/dx in terms of x and y.

Q: Q: Prove that the arc lenfth af Curve y = log secx from to n- 3 is Use formula Note I+ ( dn.

A: Given: y = log sec x To prove: The arc length of the function y from x = 0 to is .

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: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in the form y =…

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Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

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Q: ind dy/dx if y= xsquared-cotx-1divided by x squared show all work

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Q: 5. Find the length of the arc for x = 3 - Jy from y = 0 to y = 4

A:

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: 4. Use definition (not tables) of L {f(t)}= [ e"f(t)dt to find L{sin(2t)} . %3D

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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 limits sin(3t) lim In(sin(3t)) i+ In(tan(4t))" j+tln(3t) A t→0 sin(4t)

A:

Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

A:

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: I* cos z lim 1³+2

A:

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

A:

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

A: Given that: ∫14cosxxdx and n=4

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: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

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

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Q: Show that tan(arccosx) for |x| s 1, x + 0.

A:

Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

Q: Find generul solution ý +y tan (x) = see (X) - sec %3D

A:

Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2&gt;0 then…

Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

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

A:

Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.