In calculus integrals , limits and derivatives are some of the subjects . What are reasons that make these topics appealing ?

Q: Upoint Find the derivative with respect to x of 8. f(x) = ( (2x³ + 4)° + 6 ((2x³ + 4)* + 6)° + + 7.…

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Q: The derivative of the function f is defined by f'(x)=x²-3 sin (x - 5). What is the x-coordinate of…

A: Solution:

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A: Here we have,  =limx→∞3x2-9x4+2x2+1

Q: OFind the eguation of the tangent line for f(x) = 6x²-3x +a when x= 5. You may problem. use…

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Q: fx ln x dx.

A: According to the guidelines the first question can be solve in multiple question. Kindly repost…

Q: find the derivative 1).f(x)=X^3(X^4/3-1)…

A: 1)

Q: The basic idea of optimization is that we have a quantity (represented by a function), and we need…

A: The basic idea of optimization is to find the maximum or minimum of a function using the different…

Q: This problem illustrates that the derivative of a differentiable function might not even be…

A: given fx==x2sin1x   if x≠0=0            if x=0 we will the following rules 1) product rule…

Q: Which are important types of functions are frequently encountered in calculus?

A: Important types of functions frequently encountered in calculus can be categorized as follows:Based…

Q: Please solve this question using application of derivatives!!   A conical tank is designed so that…

A: the volume of the conical tank is given by the formula, V=13πr2h where r is the radius of the cone…

Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what is…

A: answer is in next step. please give a like!!

Q: The derivative of ƒ(x) = x2 is zero at x = 0, but ƒ is not a constant function. Doesn’t this…

A: Given,

Q: State the limit of the derivative f’(x) = square root of x+3, f’(2)

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Q: Please find the derivative of y = (x - xcosx)^(-1/5). I keep getting stuck with the inside function

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Q: Зx+4 3. f(x) = x2+3

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Q: Page < 11. Use f'(x) = lim x+h)-f(x) to find the derivative of f(x) = x² + 3.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the equation of the tangent line at (3, f (3)) when f (3) = 20 and f' (3) = 4. (Use symbolic…

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Q: why setting the derivative of a function equal to zero allows us to find the maximum or minimum…

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Q: Sometimes the second derivative test is harder to use, even if it applies. Use the first derivative…

A: Given,

Q: find the derivative of f(x) using the f'(x)=h(x)g'(x)+g(x)h'(x) formula and identify all parts…

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Q: how do limits relate to derivatives and integrals? also give examples of when they are used to…

A: Limit of a function is defined as , Let I be an open interval containing x0∈ℝ. Let f : I→ℝ . Then…

Q: Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of…

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Q: If the first derivative of a function equals zero when x=c, what do we know? Pick the right answer.…

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Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: 2Xin 2. O dy/dx if

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Q: Find the equation of the tangent line to the curve when x has the given value.  1. f(x) = x2 -1;…

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Q: In my most recent assignments, I've needed to take an anti-derivative of complicated formulas…

A: Let I=∫11-x20.252dx

Q: Find the derivative of the following function. You must show work for this problem. et 8(x) = x2 + 1

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Q: If a function is continuous and differentiable then its derivative continuous? True O False

A: A function, y=f(x) is continuous, if there are no holes or jumps in the graph of y=f(x) .

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: If the equation of the tangent line to the graph of the function f(x) at the point (3,-6) is 2y + 5x…

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Q: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

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Q: Find the equation of the tangent line at (3, f(3)) when f(3) 17 and f' (3) = 4. (Use symbolic…

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Q: Now, I have to apologize in advance for this question because it's quite a long one as it is 8…

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Q: 8. y= sec® (e-sin?x) |

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Q: Choose the correct value of derivative. d dx x+1 X () is equal to (Hint: Look at the note of section…

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Q: The first derivative tells how fast a function is changing. That is, for a function f(x) and value x…

A: Define second derivative

Q: Explain in your own words what the Fundamental Theorem of Calculus says. Be sure to address both…

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Q: If we need to calculate the derivative of a function at a point, there are two ways we can think…

A: Given: gx=x-x2

Q: find the derivative of the question in the picture please show all work

A: Obtain the derivative of the function.

Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given f'x=x2+2 sin2x-2. Also given f(2) = 7.   To Find: The absolute minimum value of the function f…

Q: What information can be obtained from derivatives? Please provide 2 examples from the real world and…

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Q: What is the derivative of the exponential function a x, a &gt;0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

Q: What is differential calculus? And what is the best example to understand it?

A: Differential calculus: Differential calculus is subfield of calculus. In the calculus it has two…

Q: 3. Use the limit definition of derivative to find f'(x) for f (x) = You will only get credit for…

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Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 8 and f'(2) = 3. (Use symbolic…

A: The solution is given in the next step.

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…

Q: Certain indeterminate limits such as lim were encountered in formulating many of our rules for…

A: We have to use Newton's definition of limits for finding the given limit.

Q: What have the same derivative of    f at x=5?

A: the given equation is slope of curve when a line is joining between the two point on the curve. but…