Q3. Prove that tanhz =: 1-22

Q: Ex 15: Prove that : d du tanh u = sech2 u dx dx Proof:

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Q: Ex:57 Find the FisiE of the Juuctiou sin TIt ZL oくtくし - siu -Lくtく

A: Given, The formula for the Fourier series expansion is,

Q: Evaluate e21.1.png aln(v) dx using Trapezoidal Rule with 8 equal intervals. if a = 14.49, b = 2, and…

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Q: Qoi Find y if 4+4 Cot zo

A: Given  r = √( 4 + 4cot2θ) To find y

Q: Q.4: (A) Show that Lim t'i = 4 i t >2

A: The given symbol is the symbol of the limit of the function at the given point of limit.…

Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: Find y" by imprcit differen fia fên. Simpliey unenoven Po Ssiole

A: Given:- x2 + 9y2 =9  To find:- y'' of given equation

Q: Led xe R be such thad Xn→x, show that %3D

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Q: figure th

A: 1) Here we have to find the ∠RST=?

Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: Q: If cosece - sin e = t and sece - cos e = m, prove that l'm? (12 + m2 +3) =1 1. %3D

A: Given that cosecθ−sinθ=lsecθ−cosθ=m

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

Q: Jósec? 30/3+2 tan 30d0 8.

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Q: (r(1/4)|? 4u/27 dv Prove that

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Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: Prove that 12) d SIAX 13)let y=x, find Ay/Ax

A: Derivative of function

Q: Again differentiate with sespect do 'x get we A cost- B Sinz A cosz + BSiny) { from @ d +

A: Please refer the attached image for complete solution.

Q: Find the interval on which the curv 1 y = dt 7+t+ 2t? is concave upward. Note: When using interval…

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Q: ome If y tanx, prove that y"-2(y +1)(3y+1). ir If x= sect and an

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Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: prove the following identy (sect − sin(π/2 − t))(sec(π/2 − t)−sint) = tant − tantsin2 t

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Q: 2) Find the length of the spiral: r = 0² from 0 = 0 to 0 = V5?

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Q: We have to find area right to z= 2.54

A: Given:  It is required to find the area right to z= 2.54.

Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

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

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Q: 4. Find Rable With respect ho X and X is also iable nith respect b . a ssuming fhat Y is diffrent…

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Q: const at Verify 4=(e~x-I is the gereral solticn

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Q: Find k so that dx = ke" + C.

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Q: Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O…

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Q: Given: S is the midpoint of RT, PR = PT prove: ΔPRS ΔΡΤS

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

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

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Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: Given: 41 24 Ris the midpoint of PT Prove: 2Q L 1/2 X P

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Q: ) a) Eliminate the parameter to obtain to obtain an equation in Xandy 5 describe the carve…

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Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: 4) Given: AB is an external tangent to Q0 and 0Q at points A and B, radi for O0 nd OQ are and 12,…

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Q: The volume V of a cylinder of height 4 cm and radius r is given by: V = 4ar? What is the…

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Q: ュCんーリ)キッアメー1ドつn Yeメt. フ4 (おつ ?ケ+ Find the nibimal distance between the

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Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: Use the secant mèthod to calculate V5 correct to three decimal points. fix)= heration No. S(x.)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Solve for x in the figure * AJKL is isosceles with KJ = LJ. K x+3 X-1 J 2х- 5

A: Since, triangle JKL is isosceles, so, we have, KJ = LJ

Q: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

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Q: Given: E is the midpoint of DF Prove: DE = (DF)

A: Given, E is the midpoint of DF

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.