Use one or more of the six sum and difference identities to find the exact value of the expression sin(45° - 30°).

Q: Define the term Domain and range?

A: Domain : The domain of the function is the set of values of the independent variable for which the f...

Q: Find the thousandth derivative of f(x) = xe -x

A: Given function,  f(x) = xe-x  To find the thousandth derivative of f(x) 

Q: Find the sums of the series

A: The given infinite series is: We see that,  

Q: How do you find the limit of a rational function as x→ +-∞? Give examples.

A: Rational function is the function that can be expressed in the ratio of two polynomial functions. Rx...

Q: Find the indefinite integral ∫xsinx2 dx

A: Given: The integral ∫xsinx2dx, To evaluate: The given indefinite integral.

Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

A:

Q: Illustrate the geometric idea for finding the tangent line to a curve?

A: In Geometry, A tangent line to a curve is the straight line that touches a given curve at one point ...

Q: find an equation for (a) the vertical line and (b)the horizontal line through the given point. (-1, ...

A: we have to find an equation for (a) the vertical line and  (b) the horizontal line through the given...

Q: Multiplying out, f (x) = 4x 4 - 20x 2 + 25, so f' (x) = 16x 3 - 40x = 8x (2x2 - 5). To use the Produ...

A: Solution: Consider the given function is  fx=4x4−20x2+25 The given equation can be re-written in per...

Q: Solve ,  y" - 6y' + 8y = 0

A:

Q: Evaluate x2 - 3(x - y), for x = 8 and y = 2

A: To evaluate: x2-3x-y for x=8 and y=2. To evaluating the value of expression. x2-3x-y=82-38-2=64-36=6...

Q: Is the algebraic expression a polynomial? If it is, write the polynomial in standard form : 2x + 3x2...

A: A polynomial is defined as an expression which is composed of variables, constants and exponents, th...

Q: Locate the critical points of the following function. Then use the Second Derivative Test to determi...

A: Given function is fx=x44-5x33-4x2+48x. For critical points we need to find first derivative of funct...

Q: The graph shows the height, in meters, of an eagle in terms of its time, in seconds, in flight. a. I...

A: (a) - Yes, the eagle's height is a function of time as per the graph shown.We see that as the time i...

Q: Evaluate the integrals

A: To evaluate the integral: ∫-11∫01∫02x+y+zdx dy dz Evaluating the integral: ∫-11∫01∫02x+y+zdx dy dz=∫...

Q: Evaluate the expression: 1 - 5P3/10P4

A: Consider the expression: 1-P35P410. Since Prn=n!n-r! therefore, find P35 and P410. P35=5×4×3 P410=10...

Q: If f is differentiable at a, then lim f(x) = f(a). Dー2 Select one: 0True False

A:

Q: Convert the rectangular equation 2x + 3y = 8 to a polar equation that expresses r in terms of θ.

A: Consider the provided rectangular equation, 2x+3y=8 A polar equation that expresses r in terms of θ....

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. There ...

A: Given there are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. Let initia...

Q: Geometry problems Use a table of integrals to solve the following problems. The region bounded by th...

A:

Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1...

A: To find a formula for p(x)

Q: Integrating derivatives Use integration by parts to show that if f' is continuous on [a, b], then (x...

A: Given that f' is continuous on [a, b]. Let us consider: Let f(x) be the first function and f'(x) be...

Q: Simplify : (x2 + 2)2

A: a+b2=a2+2ab+b2

Q: 59-60 - Linear Functions A linear function is given. (a) Sketch a graph of the function. (b) What is...

A: Note : As per authoring guidelines, When multiple question are posted, then only one question has to...

Q: Solve the exponential equation 9e5x = 1269. Where necessary, express the solution set in terms of na...

A: Given exponential equation 9e5x=1269

Q: Given A and b in Exercises 11 and 12, write the augmented matrix for the linear system that correspo...

A:

Q: Write the augmented matrix for the given system of linear equations.

A: Definition used -                  For a matrix equation  AX= B,                 Augmented matrix is...

Q: Determine whether the statement, '7P3 = 3!7C3', is true or false. If the statement is false, make th...

A: Prn=n!(n-r)!Crn=n!r!(n-r)!

Q: Use the basic integration rules to find or evaluate the integral

A: Given: I=∫1eln2xxdx for evaluating given integral, we substitute  ln2x=t                            ...

Q: In Exercises 11-28, use Separation of Variables to find the generalsolution. y' - ex+y = 0

A: Given: y'-ex+y=0 for finding solution of given differential equation, we use variable separable meth...

Q: Solve and check: -1 + 3 (x - 4) = 2x.

A:

Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (5,2,0) on the surfa...

A: The equation of the surface is -cosπx+2x2y+4exz+4yz=105. The function is fx, y, z=-cosπx+2x2y+4exz+4...

Q: Limits at boundary points Evaluate ху — 4у? lim (x, y)→(4, 1) Vĩ – 2Vy°

A: Given, limx,y→4,1 xy-4y2x-2y

Q: Rationalize the denominator : √2 /√5 ?

A: To rationalize the denominator of 25. Rationalizing the denominator of given expression. 25=25×55=2×...

Q: Find the distance from S(1, 1, 3) to the plane 3x + 2y + 6z = 6.

A: It is given that a point S1, 1, 3 and the equation of the plane 3x+2y+6z=6   Here x1=1, y1=1, z1=3 a...

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.