a. Use the formula к(t): = k(t): = ||r' (t) x r"(t)|| ||r' (t)||³ r(t) = e¹¹ti + e-tj to find k(t).

Q: £/ ue "du +

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Q: Example #3: Consider the function fcx) = (2x+1) √√x-1 Evaluate: a) b).. (³x f'(x) dx. 5 fcx) dx 2

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Q: Given f(u) =u/u2 - 1 and u = g(x) = 4x2 + x + 4, find (f o g)'(0).

A: Find (fog)'(x).…

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Q: Consider the function f(2) = 4z + e* +5 with g(z) - f-' (z). (a) Show that f(x) in ne-one on R. (b)…

A: (a) From the definition of one to one function, if there doesn't exist such y in its codomain such…

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Q: Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0) f(t) † (2, 2) 1

A: Handwriting solution

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Q: ren that f(x) = 6x - 6 and g(x) = 2- r', calcula f(g(0)) %3D 9(/(0)) - %3D

A: The question is taken from the above function and we have to find the composite function at the…

Q: Suppose that f′​(x)=2x for all x.   ​a) Find ​f(−4​) if ​f(0)=0. ​b) Find ​f(−4​) if f(2​)=1. ​c)…

A: Suppose that f'x=2x for all x. a To find f-4 if f0=0.b To find f-4 if f2=1.c To find f-4 if f-3=10.

Q: Use the formula £{t^f(t)} (s) = (-1)^(((s)) to help determine the following the expressions. (a) L(t…

A: Solution:-

Q: Given the following functions: f(u) = u/? and g(x) = x10 + 1. Find: f(g(x)) : f'(u) = f'(g(x)) =…

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Q: (b) Find [x² -¹ J4(x) dx in terms of Jo(x) and J₁(x).

A: In the problem we have to find the value of the integration in terms of J0(x) and J1(x).  Here we…

Q: Find f (x). f(x) = 2 In (1 + 7x?) f(x) = %3D

A: f(x)=2ln(1+x2 ) Differentiating w.r.t x both sides, we have f'(x)=2ddx (ln(1+x2))…

Q: 2ae2x 2ae2x. Let a be a real valued constant. Find the derivative with respect to x: y = -1 4xe2x O…

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Q: = f²³² € 0 Given F(x) = -t² e dt, use FTC Part II to find F'(1)

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Q: Given g(x) = In(10x° + x), the derivative g (x) is %3D

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Q: Use the table below to find h'(1) for h (x) = f (g (x)). f(2) g(z)f'(1) () 1/2 -2 2. 1. -3 0. 4 -1…

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Q: or h' (x):

A: Given that: The equation is h ( x) = g ( x 2 + f ( 3x) ).

Q: If g(t) = 1_25, then find g'(t). t

A: We will differentiate the function with respect to t to find the required

Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

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Q: £{tf""(t)} =

A: To find the laplace transform of tf''' (t) first we will use the formulae  L{tn f(t)} = (-1)n {dn…

Q: dx

A: See the details solution in below

Q: functions identical?

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Q: Let f(x)=X13, ga)= 2R-1, and h(x) : 2x* + 2n-12. Wiite a formula and Simplify for: (fh)(x)= ell

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Q: Find F(s). F(s) = L {tu(t = 3)}

A: detailed solution is given below