- 3.3.1: 116 Differentiate fx 3x f
- 3.3.2: 116 Differentiate.fx sx sin x 2
- 3.3.3: 116 Differentiate.fx sin x y
- 3.3.4: 116 Differentiate.y 2 sec x csc x 1
- 3.3.5: 116 Differentiate.y sec tan ta
- 3.3.6: 116 Differentiate.t e y
- 3.3.7: 116 Differentiate.y c cos t t2 sin t
- 3.3.8: 116 Differentiate.ft cot tet y
- 3.3.9: 116 Differentiate.2 tan x
- 3.3.10: 116 Differentiate.4y sin cos x
- 3.3.11: 116 Differentiate.f sec1 secy
- 3.3.12: 116 Differentiate.y cos x1 sin x f
- 3.3.13: 116 Differentiate.y t sin t1 t
- 3.3.14: 116 Differentiate.y 1 sec xtan x y
- 3.3.15: 116 Differentiate.fx xe s
- 3.3.16: 116 Differentiate.sin x tan x
- 3.3.17: Prove thatcsc x csc x cot x
- 3.3.18: Prove thatsec x sec x tan x
- 3.3.19: Prove thatddx cot x csc2x
- 3.3.20: Prove, using the definition of derivative, that if
- 3.3.21: 2124 Find an equation of the tangent line to the curve at the given...
- 3.3.22: 2124 Find an equation of the tangent line to the curve at the given...
- 3.3.23: 2124 Find an equation of the tangent line to the curve at the given...
- 3.3.24: 2124 Find an equation of the tangent line to the curve at the given...
- 3.3.25: (a) Find an equation of the tangent line to the curve at the point ...
- 3.3.26: (a) Find an equation of the tangent line to the curve at the point ...
- 3.3.27: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
- 3.3.28: (a) If , find and . ; (b) Check to see that your answers to part (a...
- 3.3.29: H sin H and H 3.3 Ex
- 3.3.30: f t csc t f 6 H
- 3.3.31: . (a) Use the Quotient Rule to differentiate the function (b) Simpl...
- 3.3.32: 32. Suppose and , and let tx fx sin x hx cos xf xf
- 3.3.33: 3334 For what values of does the graph of have a horizontal tangent...
- 3.3.34: 3334 For what values of does the graph of have a horizontal tangent...
- 3.3.35: A mass on a spring vibrates horizontally on a smooth level surface ...
- 3.3.36: An elastic band is hung on a hook and a mass is hung on the lower e...
- 3.3.37: A ladder 10 ft long rests against a vertical wall. Let be the angle...
- 3.3.38: An object with weight is dragged along a horizontal plane by a forc...
- 3.3.39: 39 48 Find the limit.limxl0sin 3xx
- 3.3.40: 39 48 Find the limit.limxl0sin 4xsin 6x
- 3.3.41: 39 48 Find the limit.limtl0tan 6tsin 2t
- 3.3.42: 39 48 Find the limit.liml0cos 1sin
- 3.3.43: 39 48 Find the limit.limxl0sin 3x5x 3 4x
- 3.3.44: 39 48 Find the limit.limxl0sin 3x sin 5xx 2
- 3.3.45: 39 48 Find the limit.liml0sin tan
- 3.3.46: 39 48 Find the limit.limxl0sinx 2x l
- 3.3.47: 39 48 Find the limit.limx l41 tan xsin x cos x
- 3.3.48: 39 48 Find the limit.limxl1sinx 1x 2 x 2 l
- 3.3.49: 4950 Find the given derivative by finding the first few derivatives...
- 3.3.50: 4950 Find the given derivative by finding the first few derivatives...
- 3.3.51: Find constants such that the function y A sin x B cos xA satisfies ...
- 3.3.52: . (a) Evaluate . (b) Evaluate . ; (c) Illustrate parts (a) and (b) ...
- 3.3.53: Differentiate each trigonometric identity to obtain a new (or famil...
- 3.3.54: A semicircle with diameter sits on an isosceles triangle to form a ...
- 3.3.55: The figure shows a circular arc of length and a chord of length , b...
- 3.3.56: Let . (a) Graph . What type of discontinuity does it appear to have...
Solutions for Chapter 3.3: Derivatives of Trigonometric Functions
Full solutions for Calculus: Early Transcendentals | 7th Edition
Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.
A third variable that affects either of two variables being studied, making inferences about causation unreliable
Differentiable at x = a
Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.
Point where a curve crosses the x-, y-, or z-axis in a graph.
kth term of a sequence
The kth expression in the sequence
Line of symmetry
A line over which a graph is the mirror image of itself
Measure of spread
A measure that tells how widely distributed data are.
Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b
An arrangement of elements of a set, in which order is important.
See Circle graph.
A function in which ƒ(x)is a polynomial in x, p. 158.
A statistical measure that does not change much in response to outliers.
Sum of an infinite geometric series
Sn = a 1 - r , |r| 6 1
A special form for a system of linear equations that facilitates finding the solution.
Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.