Prove the identity. cosh(-x) = cosh(x) (This shows that cosh is an even function.) cosh(-x) = | | +*)

Q: (sin -(x/ 10) dx Evaluate the integral 2 100 - x

A: Given: I=∫sin-1x102dx100-x2 for evaluating given integral, in given integral we substitute…

Q: Find the limits

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Q: True or false If cosh x = then sinh x=

A: We have cheek the statement

Q: Find the limit.

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Q: d Proof Prove that [cos x] dx - sin x. -

A: To prove ddxcos x=-sin x. In order to prove the given derivative, use the definition of derivative…

Q: ​f(x)= -2 sin 2 x on the interval [−π​,π​] Find where increasing and decreasing on the interva

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Q: Show that f is continuous on (∞ , -∞ )

A: Given Data The first function is f(x)= sin x. The second function is f(x)= cos x.   The limit of the…

Q: sin x 2. Find f'(x) if f(x) = 1 - cos x %3D 1 3. Simplify your result in (2) to show that f'(x) %3D…

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Q: lim x→0 (sin3x sin5x/x2)

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Q: sin 3x lim ,-o e-1

A: We know that

Q: Use the table to find the indicated limit.

A: Given tabular data is

Q: tan lim x+1- cos-l x

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Q: sin(7.rx) lim X-X

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Q: sin x e* -e lim Solve x→0 x – sin x

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Q: Using special limits, evaluate: 1-cos x sin x lim 0 Show your solution. 0. O undefined 01 O-2

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Q: Prove the identity. 1+ tanh(x) = e2x 1- tanh(x) 1 + cosh(x) 1+ tanh(x) 1- tanh(x) 1 cosh(x) cosh(x)…

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Q: sin(x) 4. lim x→0 1 – cos(2x)

A: The solution of the problem is given in the next step.

Q: lim x →3 (x − 3) tan(9 — x²) sin²(2x - 6)

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Q: (.0 < x < . Using the concept of Mean Value Theorem show that cos x <

A: To show: cosx&lt;sinxx2 ; 0&lt;x&lt;π2. Proof: Let fx=cosx-sinxx2. Mean value theorem: Suppose f(x)…

Q: Lim 2-2 cosx - xIn (1+x). x sin'x

A: We apply L hospital rule to find the limt. See 2nd,3rd and 4th step.

Q: Use the shown table to find the indicated shown limit.

A: The given expression is limx→0sin3xx

Q: Show that sin(x)  can be approximated by x-x3/6  within 0.01 on the interval [-1,1].

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Q: sin(3 – x) lim x→1 x2 – 5x + 6

A: Explained below

Q: QI/Solve by mean value theorem 1- F(x)=x² In the interval [1,-1] 2-F(x)=coshx In the interval [-1,3]…

A: 1) F(x)=x2. According to mean value theorem. F'(c)=-12-(1)2-1-12c=0c=0 Since, c∈1,-1. Hence , Mean…

Q: sin²(x) 2. If f(x) = - x show that the single-point method for solving f (x) = 0 will 2 converge.

A: In a single-point method, x=ϕ(x) will converge if ϕ'(x)&lt;1. Given, f(x)=sin2x2-x To show, that the…

Q: sin x 4. lim x0 et In x 6. lim

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Q: sin 5x f. lim

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Q: X 1 sin x+sin 2x Q3/ Find the value of (x) if 5 -2 1= lim %3D 3x -1 2 1

A: We will seperately find the determinant and the limit. Then, we will equate them to solve for x.

Q: sin(3x) lim x0 sin(4x)

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Q: sin(3x) 6)lim x→0 sin(4x)

A: We have to evaluate the value of limx → 0 {sin(3x)/sin(4x)}

Q: sin 2x Find lim 3x

A: given equation     limx--&gt; 0    sin(2x)/3x   ** L hospital rule :-   limx--&gt;0  f(x) / g(x) =…

Q: sin2 x cos2 4. sin x- cos4 x X - - 1 4

A: To prove that the left-hand side is equals to the right-hand side.

Q: n[-5, 7), 1-cos x Find the absolute extremum point (s) of f(x) = e- if any.

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Q: QI/Solve by mean value theorem 1- F(x)=x² In the interval [1,-1] 2-F(x)=coshx In the interval [-1,3]…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: sin 4x 18) lim X-0 tan 5x

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Q: Prove the identity. 1 + tanh(x) – e2x 1 - tanh(x) 1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 - cosh(x)…

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Q: Prove the identity. Cosh(-x)  = Cosh x (This shows that Cosh is an even function.)

A: To prove: cosh-x=coshxWe know that, coshx=ex+e-x2 Now, replacing x with -x…

Q: a) = Cos(x + a); prov

A: we have ,  sin(x-α)=cos(x+α)we have to prove that, tanx=1

Q: sin(3x) 6)lim x0 sin(4x) 4.a

A: By using the L. Hospital's law we will solve the given limit

Q: lim x -> 0    ln(1+x)-x / 1-cosx   = ?

A: To find lim x -&gt; 0    ln(1+x)-x / 1-cosx   = ?

Q: lim 1-cosx/sinx ? x--&gt;0

A: Given:

Q: cos2x – sin2x cos2x x=-F(x)+c•What is F(x)? For = - sinr

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Q: Prove the identity. cosh(-x) = cosh(x) (This shows that cosh is an even function.)

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Q: 1 + cos X 1 - cos X

A: We are given with fraction need to evaluate.

Q: sin4x 15. lim x→0 sin7x

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Q: sin(6x) Evaluate: lim 1-oL sin( 4x) A B0 1

A: we have given that limx→0[sin(6x)/sin(4x)]

Q: 4-x Find the domain range of the function f(x) = sin log 1-x

A: