h(x) = coth-1(x)      if       x>=1           [[x+1]]           if        -1 <  x  <  1           tan-1 (x2+2x+1)        if          x<= -1 Is h continuous at x=-1, 0, and 1? If not, Is it removable, jump essential, or infinite?

Q: Suppose the derivative of a function f is Then f(x) is decreasing on the following interval: ○ (1,4)…

A: A function fx is said to be decreasing on an interval a, b if fx≤fy whenever x≤y and fx is said to…

Q: * +(x) = 3x6-4 (x-k)² +17, the value of the parameter k for f(x) to be a function pair IS?

A: For f(x) to be a function pair  it needs to be one-to-one, which means that each input value must…

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: Graph ƒ(x) = tan-1 x + tan-1(1/x) for -5&lt;=x&lt;=5. Then use calculus to explain what you see. How…

A: Simplify the function first in order to make its graph look easier, which can be done using…

Q: Suppose that ƒ′(x)&lt;= 1 for 1&lt;= x&lt;= 4. Show that ƒ(4) - ƒ(1)&lt;=3.

A: Show that:

Q: Q1: In Leibnitz theorem, If f and g are functions of a variable x, then nth derivative of (f.g) can…

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Q: Find the derivatives of the follwing function f(x) -4 i)e log(3x+4) x>. 3 )(4+x*)e* ax+b iii.…

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Q: On which of the following intervals is the function f(x) = x3 differentiable? (0, +∞0) 0 (-00, +∞0)…

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Q: f(x) = ln(3x + 5). Show with induction that the n-derivative of f is given with "the function from…

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Q: prove that f(x) = sin*x + cos*x is a periodic function with periods

A: We use the Given Equations Prove that f(x) is a periodic function with period pie/2.

Q: Let g(x) be a continuous function and let g(") (x) be the n-th derivative of g(x). Find an example…

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Q: Suppose f(x) = 3*sec(3*) tan( 3*). Evaluate: / s(x)dx sec(3*) A +C In (3) 3*. sec(3*) +C B In (3) ©…

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Q: 22. State True or False. Let f(x)=sin'(x) + log(x) then domain of f(x) is (-*, ). a) True b) False

A: To check whether the statement is true or not. The statement is Let f(x)=sin2x+logx then domain of…

Q: Assume that h[n]=(-1)"g[n]. What is the relation between H(2) and G(z) o HZ) = (- 1)" G(z) H(2)…

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Q: Find “a & b” if f(x)=x^2+4x+a x>0 ; f(x)=bx x<0 ; f(x)=f(0) x=0 is continuous at every

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Q: Which of the following is a function whose graph is continuous everywhere except at 3 and is…

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Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

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Q: Suppose and Then ((fog) – (g°f))(x) =| f(x) = g(x) 8 x+1 x+1 8

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Q: Let f(x) = ²-7x-18 ✩ if x = -2 if x=-2 Is f continuous at x = -2?

A: A function is said to be continuous at x=a if limx→a-f(x)=limx→a+f(x)=f(a)…