What is the first derivative of f(x) = Answer: f'(x) = 8 + 7 ln(x)? What is the slope of the line tangent to f(x): decimal places? Answer: m = 8 +7 ln(x) at the point (4, 10.204) rounded to 3 x²

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A: We have to find the value of limit of the given function.

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A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: The given functions are

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A: Since first two subparts are already solved , i solved the third subpart

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A: we need to find out the derivative of the given function."Note that as per the rules, we are…

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A: Let  be a continuous function and set To evaluate the following.

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A: By finding the first four terms, we can then find the first four partial

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A: Given, .we know, .

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A: By using differentials to approximate the value of the following expression.To compare the answer…

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A: Given,  F(x)=f(f(x)) and .Given, f(3)=9, f(9)=3, f'(9)=4, f'(3)=15

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A: Given, .we know,

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A: Given,

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A: we need to find out the intervals where the function is increasing and the interval where the…

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A: given function

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A: Given, final value= $368302.35.Given, rate= 21%.Given, time= 4 years.Formula for compounding…

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Q: - 3x - 4 f(x) = { x² - 2 2x − 3 - if x < -1 if −1 < x < 1 if x ≥ 1

A: To graph the following function.

Q: Evaluate lim (10x³ – 7x + 14). 21 (1023 lim (10x3 7x+14) = x→-1 = Number

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Q: 1. Given the equation that describes 1 y=-(x-2)² +27, determine: a) the vertex b) the domain and…

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Q: d) lim √2-x X-2+ 4 e) lim (¹2) x-3x-2

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A: Using the given graph we can identify all the local and absolute extreme points

Q: Evaluate the limit using L'Hôpital's rule, if applicable. 13x² e5x lim x →∞

A: we need to find out the limit.

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A: Using application of derivatives we can find the maximum value

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Q: 3. Differentiate the following functions and state whether they have maxima or minima. a) y =…

A: Note:-Since you asked multiple questions which are not interlinked, according to our policy we can…