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The Hyperbolic Sine, Hyperbolic Cosine & Hyperbolic Tangent
The Inverse Hyperbolic Cotangent, Hyperbolic Secant & Hyperbolic Cosecant
Remember Logarithmic Identities ( Calculus I )
Logarithmic Identities II
Proofs Identity (1)
Proofs Identity (2)
Proofs Identity (3)
Proofs Identity (4)
Proofs Identity (5)
Proofs Identity (6)
Proofs Identity (7)
Derivatives of Hyperbolic Functions
Proofs (1) (sinhx)’ = coshx (2) (coshx)’ = sinhx
Proofs (3) (tanhx)’ = sech2x
Proofs (4) (cothx)’ = -csch2x
Proofs (5) (sechx)’ = - sechx tanhx
Proofs (5) (cschx)’ = - cschx cothx
Integrals Involving hyperbolic Functions
Graphs of Hyperbolic Functions
Graphs of Exponential Functions Functions
Graphs of Exponential Functions
f(x) = Cosh x
f(x) = cosh x = (½)ex + (½) e-x as x → ∞ the values f(x) → ∞ following (½)ex as x → - ∞ the values f(x) → ∞ following (½) e-x
f(x) = sinh x
f(x) = tanh x
f(x) = secx
Differentiation of Hyperbolic Functions. Differentiation of Hyperbolic Functions by M. Seppälä Hyperbolic Functions.
Inverse Trigonometric Functions
The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.
6.5 & 6.7 Notes Writing equations of trigonometric functions given the transformations.
A Library of Functions This presentation will review the behavior of the most common functions including their graphs and their domains and ranges. See.
Properties of the Trigonometric Functions. Domain and Range Remember: Remember:
MTH 252 Integral Calculus Chapter 7 – Applications of the Definite Integral Section 7.9 – Hyperbolic Functions and Hanging Cables Copyright © 2005 by Ron.
Trigonometric Functions on Any Angle Section 4.4.
Inverse Hyperbolic Functions. The Inverse Hyperbolic Sine, Inverse Hyperbolic Cosine & Inverse Hyperbolic Tangent.
Graphs of the Other Trigonometric Functions Section 4.6.
Reciprocal Trigonometric Functions. Reciprocal The Reciprocal of any number x is: Ex: Find the reciprocal of 0.5x 2 Equivalent forms of this definition:
Inverse Trigonometric Functions The definitions of the inverse functions for secant, cosecant, and cotangent will be similar to the development for the.
Chapter 3 – Differentiation Rules
Hyperbolic Functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2005 Scotty’s Castle, Death Valley, CA.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A Concise Introduction to MATLAB ® William J. Palm III.
Copyright © Cengage Learning. All rights reserved. 6 Inverse Functions.
Hyperbolic Trig Functions Greg Kelly, Hanford High School, Richland, Washington.
3.5 – Derivative of Trigonometric Functions
5.9 Hyperbolic Functions. Graph the following two functions: These functions show up frequently enough that they have been given names. The behavior of.
Warm-up:. Homework: 7.5: graph secant, cosecant, tangent, and cotangent functions from equations (6-7) In this section we will answer… What about the.
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