I need help with question 21 in Section 3.

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Use the definitions of the hyperbolic functions to find each of the following limits. Prove the formulas given in Table 1 for the derivatives of the functions a cosh, b tanh, c csch, d sech, and e coth. Give an alternative solution to Example 3 by letting y sinhx and then using Exercise 9 and Example 1 a with x replaced by y.

Prove Equation 4. Prove Equation 5 using a the method of Example 3 and b Exercise 18 with x replaced by y. For each of the following functions i give a definition like those in 2ii sketch the graph, and iii find a formula similar to Equation 3. Prove the formulas given in Table 6 for the derivatives of the following functions. Simplify where possible. If tanh x 1, find the values of the other hyperbolic func- Questions are typically answered within 1 hour.

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Q: Let f t be the temperature at time t where you live and suppose that at time t 3 you feel uncom Two runners start a race at the same time and finish in a tie. Prove that at some time during th Q: Use the Fundamental Theorom of Calculus to write the number 26 as an integral. If I pick the l A: 1 Write the number 26 as an integral.

Q: Find and sketch the domain of the function included in the image. Q: how do you solve this problem? Q: Find an equation for the level curve of the function f x,y that passes through the given point.

Then find the exact values. Estimate t Q: Can you help me with this problem step by step?I need help with Calculus HW.

I need to differentiate problem 25 on pageSection 3. I need help on simplifying the problem. Do your answers agree? Find the derivative of the function Find an equation the specified point. Show that your answers are equivalent. Which method do Find equation you prefer?

If f If At xe Su Questions are typically answered within 1 hour. A: To sketch the graph of the function and determine its range and domain.

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Give your A: We use the definition of limit to find the derivative. A: Before we go to find the symmetry of the given figures, let us know the meaning of symmetry about x Q: Use the General Power Rule to find the derivative of the function. Subscribe Sign in. Operations Management.

Chemical Engineering. Civil Engineering. Computer Engineering. Computer Science. Electrical Engineering.The idea of flipping the order of learning needs and curriculum development is definitely counter-intuitive to me.

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## Chapter 3 - Differentiation - 3.9 Related Rates - Exercises - Page 159: 14

Cellular Biology. Earth Science. Environmental Science. Life Science. Marine Biology. Organic Chemistry. Periodic Table. Physical Science. Plant Science. American Literature. British Literature. Creative Writing. Medieval literature.I need help with question 15 in Section 3. Use the definitions of the hyperbolic functions to find each of the following limits. Prove the formulas given in Table 1 for the derivatives of the functions a cosh, b tanh, c csch, d sech, and e coth. Give an alternative solution to Example 3 by letting y sinhx and then using Exercise 9 and Example 1 a with x replaced by y.

Prove Equation 4. Prove Equation 5 using a the method of Example 3 and b Exercise 18 with x replaced by y. For each of the following functions i give a definition like those in 2ii sketch the graph, and iii find a formula similar to Equation 3.

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Prove the formulas given in Table 6 for the derivatives of the following functions. Simplify where possible. If tanh x 1, find the values of the other hyperbolic func- Questions are typically answered within 1 hour. Q: For the given function find the average rate of change over each specified interval. A: Distribute tan x. Q: Express the given quantity as a single logarithm In x 2 7 In x In x23x 2 2 2.

A: Make the coefficients into exponent. And they will multiply with the existing exponents. Q: Find the equation of the tangent line to the curve at the given point using implicit differentiation A: To determine the equation of tangent line to the given curve at point 1, 0. Q: Consider the following.

Q: The concentration, y, of a drug in the bloodstream t seconds after injection into a muscle is given A: To determine the maximum concentration of a drug in the bloodstream. Use the following graph of the functionf to find the A: According to the given two points that lie on tangent are:. Subscribe Sign in. Operations Management.

Chemical Engineering. Civil Engineering.

### Differentiation & the Brain - Chapter 3: Curriculum

Computer Engineering.AP Calculus AB. AP Research. Calculus Geometry L2 Geometry L3. Sanjay Rambhia. Frosh Schedule. Junior Varsity and Freshmen Rosters. Outstanding Performances. Sub Varsity Schedules. Varsity Roster.

Varsity Schedule. Sequences and Series. Tangents and Angle Relationships in Circles. Given a graph of a function, students should be able to graph the derivative of the function.

Practice on Derivatives. Progress Check - Derivatives. Graphing Derivatives given the graph of f xand Differentiation. Worksheet - Derivative of Trig. Worksheet - Chain Rule. Worksheet - Implicit Differentiation. Worksheet - Extra Practice on Implicit Differentiation. Review Sheet for Chapter 3 Test Part 1. Exponents and Logarithms section 3. Trig Inverse Derivatives. Graphing f from f IC. Sanjay Rambhia, Oct 5,PM.We have already studied how to find equations of tangent lines to functions and the rate of change of a function at a specific point.

In all these cases we had the explicit equation for the function and differentiated these functions explicitly. Suppose instead that we want to determine the equation of a tangent line to an arbitrary curve or the rate of change of an arbitrary curve at a point.

In this section, we solve these problems by finding the derivatives of functions that define y y implicitly in terms of x. In most discussions of math, if the dependent variable y y is a function of the independent variable xxwe express y in terms of x. If this is the case, we say that y y is an explicit function of x. On the other hand, if the relationship between the function y y and the variable x x is expressed by an equation where y y is not expressed entirely in terms of xxwe say that the equation defines y implicitly in terms of x.

Implicit differentiation allows us to find slopes of tangents to curves that are clearly not functions they fail the vertical line test. We are using the idea that portions of y y are functions that satisfy the given equation, but that y y is not actually a function of x. In general, an equation defines a function implicitly if the function satisfies that equation. An equation may define many different functions implicitly. For example, the functions.

However, it is not always easy to solve for a function defined implicitly by an equation. Fortunately, the technique of implicit differentiation allows us to find the derivative of an implicitly defined function without ever solving for the function explicitly. The process of finding d y d x d y d x using implicit differentiation is described in the following problem-solving strategy.

To perform implicit differentiation on an equation that defines a function y y implicitly in terms of a variable xxuse the following steps:. Note that the resulting expression for d y d x d y d x is in terms of both the independent variable x x and the dependent variable y. Although in some cases it may be possible to express d y d x d y d x in terms of x x only, it is generally not possible to do so.

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In Example 3. We can take the derivative of both sides of this equation to find d 2 y d x 2. At this point we have found an expression for d 2 y d x 2. Now that we have seen the technique of implicit differentiation, we can apply it to the problem of finding equations of tangent lines to curves described by equations.

Although we could find this equation without using implicit differentiation, using that method makes it much easier. This curve is known as the folium or leaf of Descartes.

Begin by finding d y d x. The rocket can fire missiles along lines tangent to its path. The object of the game is to destroy an incoming asteroid traveling along the positive x -axis toward 00. If the rocket fires a missile when it is located at 38 538 5where will it intersect the x -axis? To solve this problem, we must determine where the line tangent to the graph of. Begin by finding d y d x d y d x implicitly.

The missile intersects the x -axis at the point 25 30. For the following exercises, use implicit differentiation to find d y d x. For the following exercises, find the equation of the tangent line to the graph of the given equation at the indicated point.