-5 -3 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

Q: Use the Quotient Rule to find the derivative of the function.                                f(t) = ...

A: the quotient rule of the derivative states dydt=v.dudt-u.dvdtv2 here v=t3,u=cost we will derivate it...

Q: A piecewise function is shown. Use the function to find the shown indicated limit, or state that the...

A:

Q: Find all solutions of the equation in the interval 0, 2n). V3 cot0-1=0

A: Given equation - 3cotθ-1 = 03cotθ = 1cotθ = 13Here, the value of cot is positive, and cot is positiv...

Q: Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the gra...

A: given the rational functions f(x) = x/(x - 3). We need to find the vertical asymptotes for the above...

Q: If P1 = (-2, 3), P2 = (-1, 5), and v is the vector from P1 to P2. Solve, a. Write v in terms of i an...

A: P1-2, 3 & P2-1, 5   a. v=-1--2i+5-3j   ∵Vector v with initial point a, b & terminal point c,...

Q: the graph of ƒ' is given. Determine x-values corresponding to inflection points for the graph of ƒ.

A: Given       

Q: Determine whether the statement makes sense or does not make sense, explain your reasoning. Knowing ...

A:                                  (3x2y)2 can be written as (3)2(x2)2(y)2=9x4y2Reason: Yes!  here we ...

Q: An integrand with trigonometric functions in the numerator and denominator can often be converted to...

A: Given We have to evaluate

Q: In which variable(s) should you complete the square to identify the surfacex = y2 + 2y + z2 - 4z + 1...

A: We have to determine which variable should we complete the square to identify the surface x=y2+2y+z2...

Q: Suppose that 0< c < π/2 . For what value of is thearea of the region enclosed by the curves  y...

A: Consider the given: y=cosx,y=cosx−c and x=0cosx−cosx−c=0−2sin2x−c2sinc2=02x−c2=0x=c2 Find the area: ...

Q: Find the domains of f and f−1 , (a) find the ranges of f and f−1 , (b) graph f and f−1 , and (c) sho...

A: Given: f(x) = 3-4xf-1(x) = 3-x4 

Q: The average weight, W, in pounds of an adult is a function, w = f(c), of the average number of calor...

A: (a) f(1800)=155this implies calories is 1800 and weight is 155.so, the average weight 155, in pounds...

Q: State the method of integration you would use to find each integral. Explain why you chose that meth...

A: ∫x2x2+1 dx

Q: The equation for f is given by the simplified expression that results after performing the indicated...

A: This is the equation for f.

Q: True or false: A function can have more than one y-intercept.________

A:     The statement is:  A function can have more than one y- intercept._________    

Q: By using appropriate substitution and then trigonometric substitution to evaluate the integral. 2 1....

A: Use the substitution u=et+9, to simplify the integrand and then use the formula ∫xndx=xn+1n+1+C, to ...

Q: Limit proofs Use an appropriate limit definition to prove the following limits. lim V4x - 8 = 0 xS2*

A: we have to use an appropriate limit definition to prove the given limit limx→2+4x-8=0 L.H.S: as we k...

Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line. (I...

A: Horizontal tangent means slope of a line is equals to 0 Given, y=x+5ex

Q: Consider the following function on the given interval [a, b].a. Determine whether the Mean Value The...

A: Mean value theorem: Let f(x) is any function that satisfy both of the following, 1) f(x) in continuo...

Q: 35. /2.1 – V2 is larger than /9.1 – ỹ.

A:

Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of 1- 1?

A: Ix=2x-18 Now let, y=2x-18 Now to find inverse function interchange x and y, then solve for y in term...

Q: Find the area inside the circle r = 2cosθ and outside the unit circle r = 1.

A: Given that: r=2cosθ  and   r=1 To calculate the intersection points, 1=2cosθcosθ=12θ=π3   and   -π3 ...

Q: Find parametric equations for the lines in The line through the point (3, -2, 1) parallel to the lin...

A:

Q: Find the partial fraction decomposition of (4x2 + 5x - 9)/(x3 - 6x - 9)

A:

Q: Integration by Substitution Integration by Parts Integration Using Trigonometric Identities Integrat...

A: Use the trigonometry identity cos2x=1-sin2x and then substitute u=sinx and factorize the denominator...

Q: The following figure shows the depth of water at the end of a boat dock. The depth is 5 feet at high...

A: If y=AcosBx+C+D Where Amplitude = A Period = 2πB Phase shift = C Mid line y = D

Q: Calculate the first quadrant area bounded by the following curves: y=x²+2, y=4 and x=0.

A:

Q: Partial derivatives Find the first partial derivatives of the following functions.

A: the given function is: gx,y,z=xyzx+y we have to find the first partial derivatives of the given func...

Q: Evaluate the integral.

A:

Q: a. Find the open intervals on which the function is increasing andthose on which it is decreasing.b....

A: Maxima or minima: Let f(x) is any function, 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate f'...

Q: Explain how to factor x3 + 1.

A: To explain how to factor x3+1.

Q: 30 dx (4x+1)3/2

A: Given: ∫1630dx4x+132

Q: Determine whether each graph is the graph of an even function, an odd function, or a function that i...

A: Given that : Graph of the functions :  

Q: How do you determine the absolute maximum and minimum valuesof a continuous function on a closed int...

A: Let f be a continuous function in a closed interval a,b. We will Evaluate f at all the critical poin...

Q: Perform the indicated matrix operations:

A: -4  3  7-6+6-32-4

Q: Show that the sum of the squares of the direction cosines of a line through the origin is equal to 1...

A: To show: The sum of the squares of the direction cosine of a line through the origin is equal to 1.

Q: Use a graphing utility to graph the polar equation over the given interval. Use the integration capa...

A: Given r = 2 sin(2 cos θ), [0, π]