For Exercises 27–32, evaluate the trigonometric function at the given real number. 5T 11T 27. f(t) = cost; t = 3 28. g(1) = sint; t = 4 29. h(t) = cott; t = 6. 57 30. s(t) = sec t; t = 3 57 32. r(t) = tan t; t = 6 31. z(t) = csct, t =

Q: b) Prove that 2 < (1+1/n)" < 3 for all n e N Your answer

A: Solution: Consider the given  2≤1+1nn≤3  for all n∈ℕ Let an = 1+1nn, ∀n∈ℕ Then we have to show that ...

Q: Find the areas of the regions enclosed by the two curves y = x - 6 and y = 3.

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: Solve the equations |((3 Z )/2)-1|≤2

A: The given inequality is 3z2-1≤2. Solve this as follows.  

Q: Q2. Find the general term of the sequence, starting with n=2 and test for convergence. (12 – J5) (13...

A:

Q: Q.2: Solve the equation using the synthetic division: 3y +5y +10y-4=0

A:   Given :           3y3 + 5y2 + 10y - 4 = 0   To solve the given equation using the synthetic divisi...

Q: please answer using Integration Technique-Ratoinal Fraction

A:

Q: 10. True or False The slope of a nonvertical line is the average rate of change of the linear functi...

A: true

Q: Sketch the domain of the function.  f (x, y) = √(81 − x^2)

A: Sketch the domain of the function.       fx,y=81-x2

Q: Let N(t) be the percentage of a state population infected with a flu virus on week t of an epidemic....

A: The percentage estimated population would be N(4)=N(3)+N'(3) As(N'(3)=N(4)-N(3)4-3=slope So N(4)=8+1...

Q: ?= 2/3?(3?−5)^4 Find?′

A:

Q: If 3 + 4i is a zero of a polynomial function of degree 5 withreal coefficients, then so is .

A: Since, we know that if a+ib is a complex zero of a polynomial withreal coefficients, then its comple...

Q: find the linearization L(x) of ƒ(x) at x = a.ƒ(x) = sqrt(x2 + 9), a = -4

A: Given function is, fx=x2+9, a=-4.   The objective is to linearize Lx of fx at x=a.   It is known tha...

Q: 4

A: NOTE*** As per bartleby guideline for more than one question asked only first is to be answered plea...

Q: How is the addition formula used in deriving the formula (sin x)' =cos x?

A: Addition formula: sinA+B=sinAcosB+cosAsinB  

Q: Which of r = 2 sec θ and r = 2 csc θ defines a horizontal line?

A: we have to tell which of r = 2 sec θ and r = 2 csc θ defines a horizontal line.

Q: Solve for the critical points of parametric equation x=t^3-1, y=t^2+t

A:

Q: Convert the following radian measures to degrees.

A: We have to convert the given radian into degree: -13π6 We know the relation between radians and degr...

Q: sketch the graph of a function f whose derivative f' has the given description:f'(x) &gt; 0 for x &g...

A: Given that f'(x) &gt; 0 for x &gt; 3 and f'(x) &lt; 0 for x &lt; 3. There are many possible graph to...

Q: 12. Find the center and radius of the circle x² + y² + 4x – 2y – 4 = 0. Graph this circle.

A: x2+y2+4x-2y-4=0

Q: Determine where the local and absolute maxima and minima occur on the graph given. Assume domains a...

A: We have given a graph . We have to find the local and absolute maxima and minima on the graph.

Q: In terms of relative growth rate, what is the defining property of exponential growth?

A:     To explain the defining property of exponential growth in terms of relative growth rate.

Q: 11. Let m(x) = Ax" be a power function. Evaluate lim m(x)'/x X00

A:

Q: Establish each identity.

A:

Q: Graph the functions in Exercises 25–28.

A: "Since you have posted a question with multiple sub-parts,we will solve the first three sub-parts fo...

Q: 33. Building's Shadow On a morning of a day when the sun will pass directly overhead, the shadow of ...

A:

Q: find the first and second derivatives

A: Given expression: w=3z7-7z3+21z2

Q: What is the domain of the cosine function?

A: Domain are the set of values for which the function exist . The time period of cosine function is 2π...

Q: Describe the domain and range of the function.  f (x, y, z) = xz + e^y

A:

Q: In Exercises 33–38, a. Use the Leading Coefficient Test to determine the graph's end behavior. b. De...

A: 33. Given  The equation is  fx=x3-x2-9x+9 .

Q: Determine whether the function is even, odd, or neither: (a) f(x)= x* – 3x² (b) g(x) = sin(x + 1) (c...

A: To determine whether the function is even , odd or neither, (a) f(x)=x4-3x2 (b)g(x)=sinx+1 (c) f(x)=...

Q: The velocity components at point (2, 2) is specified by the equation u = x1 + 3y and v = - 2xy. Dete...

A:

Q: What is the Market equilibrium point of the 2 functions? x-y+1=0 and 6x+10y-42=0 a.) (2,3)b.) (-3,2)...

A: Solution:Given  x-y+1=0 and     6x+10y-42=0  

Q: Liza is a basketball coach and must select 5 players out of 12 players to start a game. In how many ...

A:

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4  

Q: find an equation of the conic described. Graph the equation Hyperbola; center at ( - 2, - 3); focus ...

A: Explanation: A hyperbola: Center: (-2,-3)Focus: (-4,-3)Vertex: (-3,-3) Formula Used: Equation of hyp...

Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at (12,12,1...

A:

Q: use the formal definition of limit to prove that the function has a continuous extension to the give...

A: Recall the formal definition of the limit to prove the result as follows: limx→3fx=limx→3x2-2x-32x-6...

Q: Let f(x)=x4 + 1/3 x3 - 7x2 Identify the x-coordinate of inflection point(s) on the graph of f.

A: f(x)=x4+13x3-7x2 A point of inflection is found where the graph of a function changes concavity. Alg...

Q: Q.1: The length of rectangular piece of paper exceeds its breadth by 5cm. If a strip of 0.5cm wide b...

A: The area of a rectangle is equal to the product of its length and breadth. Let the length and the br...

Q: solve log5 18

A: The given logarithmic expression is, log518. The objective is to solve the expression.

Q: Which of the following is not a meaningful triple integral?

A: a. ∫01∫0x∫x+y2x+yex+y+z dz dy dxb. ∫01∫0z∫x+y2x+yex+y+z dz dy dx

Q: xy sin y dAR: - 3sXs3, 0sysn SSwsiny dA= xy sin y dA =

A: Use double integration to evaluate it

Q: 3 cos + csc Find the exact value of tan

A: There are 6 Trigonometric functions defined as sine, cosine, tangent, cosecant, secant and co-tangen...

Q: Determine the amplitude and period of each function without graphing. y = 6 sin(π x)

A: The general equation of the sine function is y=Asin(Bx), where A is the amplitude and 2πB is the per...

Q: Let f(x)=x4 + 1/3 x3 - 7x2 a. Identify the interval(s) where f is increasing. b. Identify the interv...

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

Q: 119. If f(x) = a*, show that f(A + B) = f(A) • f(B).

A: Given: fx=ax For finding fA+B, we put x=A+B in given expression and simplify it

Q: Write each expression as a single logarithm

A: Given,

Q: Find real values of x for which f(x) = 0. f(x) = 4x + 6

A: To find the real values of x for which fx=0. Solution: Put fx=0 and solve for x. 4x+6=04x=-6x=-64x=-...

Q: Use Newton's method to approximate the value of 591/3 as follows:Let x1=3 be the initial approximati...

A: Let's consider a function whose zero is 591/3 and solve it using Newton's method.