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Q: Find the derivative of the function in the following two ways. x4(x6 + 1) (a) Find the derivative ...

A: Calculation:Let f(x) = x4(x6 + 1)(a)Compute the derivative of f(x) using the product rule as follows...

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A: The 190 grams of the radioactive isotope that remains after first half life is computed.

Q: 45. A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec....

A: Consider the given height as a function of horizontal length:

Q: (c) The following limit represents the derivative of some function f at some number a. State such an...

A: The derivative of the function is defined by,

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A: Obtain the value of f(–2/3) as follows.

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A: Domain is the set of all the input values for which the given function is defined.Range is the set o...

Q: Using the intermediate value theorem, show the given function has a solution.

A: Calculation:Simplify the given equation as 2x + 3x – 4x = 0.Consider f(x) = 2x + 3x – 4x.

Q: Please differentiate the functions provided in the two images

A: (i) The given function is

Q: Use the properties of logarithms to ﬁnd the exact value of the expression. Do not use a calculator. ...

A: The known facts: