ALWAYS true, SOMETIMES true, or NEVER true x+1< x x> 2* 42>24 1+1<2! Sometimes true X'< (x - 1)"*1 if xis a small number, and yis a large one

Q: lim (1-cos x1/2) / ln(1+x) ? x--&gt;0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

A:

Q: Determine whether the equation is true or false: ln(5x) + ln 1 = ln(5x). Where possible, show work…

A:

Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

A:

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: 1. lim 3" 5. lim tan r 2. lim 5 6. lim cos r 3. lim log r 4. lim cos r 7. lim sinr

A:

Q: Find the root of fx)=ln(x)-cos(x) by Newton Raphson method take xo-0.5 Bisection method (1, 2)…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: sech (In x*) 15. dx x/6 tanh (In x2) – tanh? (In x2)

A:

Q: Find an equation of the tangent line at x = 0. y = x5 + cos(x) .13 (Use symbolic notation and…

A: We have given equation  y=x13+cosx Put x=0  y=0+cos(0)=1 Point on the curve x1,y1=0,1…

Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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Q: Find the derivative and show your complete solution of the following 1. cos(e ^ (2x) + e ^ (- 2x))…

A:

Q: sech (x*) tanhl 12.

A: 12. Given integral is ∫sech3(x13) tan h(x13) x23dx Let us make substitution to simplify the above…

Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

A:

Q: 2 1- cosh-1 x = In(x+Vx² –1 2- coth¬lx = x+1 In 2 x-1 Vi+x? 1 3- csch hx= ln(÷+

A:

Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

A:

Q: FIN 2 dx

A: Note:- In given problem, according to written way sin2x is multiplied by 3x+1. If you want solution…

Q: 4. Given that x³ - x - 1 has a root between 1 and 2 Find the root to four decimal places using…

A:

Q: x* +00 + 3 -dx x² + 3x + 1 -00 8

A: Note that for x&gt;3 and x&lt;-3, x4+3x2+3x+1&gt;x. Now, ∫-∞∞xdx diverges so, ∫-∞∞x4+3x2+3x+1dx…

Q: 3. sin(3x) = 3s in x – 4sin³ x

A:

Q: 16 |how do you express limn→0 0 Li=1 - (5+ £)9/ as п definite integral

A:

Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

Q: If f(x)=tanh^-1 square root x to the fourth power then f'(x)=

A:

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: 3. Show that Σ L 1 L-x= 2 2nnx sin L 0<x<L.

A: Let f(x)='12L-x Fourier half range sine series in 0&lt;x&lt;L is bn=2L∫0Lf(x)sinnπxLdx…

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

A:

Q: 2. 2. COS X Sinx lim 4x-X

A:

Q: 2* csch (2*) cosh(2*)-sinh(2*)

A: We have to find the value of integral

Q: l = lim x→0+ In(x)

A: No, its wrong. you are correct limx→∞ln(x)=-∞…

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: The given integral is ∫sinh54xcosh4x dx. We have to check whether the given integral can be…

Q: The equation xsin x + cos x =1.015 has a positive root a close to zero. Use small-ar approximations…

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Q: 1 1- (-1)". f (x) = 2 sin nx. - n=1

A:

Q: 1. sin x sin 2x + cos x cos 2x = COS X

A:

Q: - Find All solutions. For y = 3.0 to the Transcendental equation. sinx-ln z = X - Y + gamma x & This…

A: note : the last term in the given transcendental equation is "gamma" which is used to represent the…

Q: 1 + X tanh (x) 1 In 2 - 1 - X

A: The solution is given as

Q: /sin³(x)(2x+5)6 ex4-5 3 . Find y' if y = %3D (ex*-5) ' log4(2x)

A:

Q: How do I solve the limit as x goes to -1 for the expression (sin(3x-3))/(1-x) without using…

A: The given limit is,

Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

A:

Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: sinh- x = In 2.

A:

Q: How large do we have to take x so that 1/x

A:

Q: 4. Find all values of x satisfying In[(2x + 1)(x + 2)] = 2 ln(x + 2). Verify the values of x you…

A: The given equation is  ln[(2x + 1)(x +2)]= 2ln(x+2)

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: 9. 1 dx - 3

A: Solution

Q: 1. f(x) = cos 2x - Show the solution of the derivative using F'el trigonometric identity that it…

A:

Q: 1. lim sin x sin 2x x-0 1-cos x 3x+x+2 . lim X-4x3+8x+1

A: d) To evaluate                       limx→0 sin x sin 2x1- cos x                            =sin (0)…

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: sech2(In x)

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.