In Exercises 1-16, calculate y" and y". y = 51-3 + 71-8/3 + 7t°

Q: What can be said about f (3) if f is continuous andlim f(x) = ½? x→ 3

A: Given that, the function f(x) is continuous and limx→3fx=12. Since, function f(x) is continuous in w...

Q: The graph of y = A sin Bx has amplitude =_____ and period =______.

A: We have to fill in the blanks: The graph of y=A sin Bx has amplitude =_____ and period =______. We k...

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = sin x + sec...

A: y=sinx+secx,  y=0,  x=0  &  x=π3

Q: Solve the logarithmic equation log2(x - 6) + log2(x - 4) - log2 x = 2. Be sure to reject any value o...

A: we have to solve the logarithmic equation log2(x - 6) + log2(x - 4) - log2 x = 2.  

Q: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture c...

A: we have been given that You are dealt one card from a standard 52-card deck. we have to find the  pr...

Q: 55. * = 2

A: To Show ∑n=1∞n2n=2

Q: Express each of the following products as a sum or difference: a. sin 5x sin 2x   b. cos 7x cos x.

A: We have to express as a sum or difference for the products: a. sin 5x sin 2xb. cos 7x cos x We know ...

Q: Express the function in the form  f ° g   F(x ) = cos x2

A: Given that, F(x) = cos (x^2) Let us consider, f(x) = cos x g(x) = x^2

Q: Write the first three terms in the binomial expansion, (x + 2)8 expressing the result in simplified ...

A:

Q: Use a sketch to find the exact value of the expression cos (sin-1 4/5)

A: given expression: cossin-145we have to find the exact value of the expression

Q: Asap

A:

Q: Write the equation of a rational function f(x) = p(x)/q(x) having the indicated properties, in which...

A: Rational function f has a vertical asymptote given by x=3, a horizontal asymptote y=0, y-intercept a...

Q: Solve ,  y"-12y'+35y = 0

A: We have to solve  y" - 12y' + 35y = 0  (D2 - 12D + 35)y = 0 The auxiliary equation is  m2 - 12m + 35...

Q: x3 - 10x - 12 = 0 a. List all possible rational roots.b. Use synthetic division to test the possible...

A: Given x3 .- 10x - 12 = 0 We need to : a. List all possible rational roots.b. Use synthetic division ...

Q: Graph: f(x) =(4x - 4)/(x - 2).

A: Given function is fx=4x-4x-2. Given function can be simplified as: fx=4x-4x-2=4x-1x-2 Since, degree ...

Q: BY remainder theorem find the remainder when p(x) is divided by g(x)  p(x)=x3-2x2-4x-1 g(x)=x+1

A: Here p(x)=x3−2x2 −4x−1 and g(x)=x+1   Now, p(x) is divided by g(x) g(x)=0 x-1=0 x=-1 Put this -1 ins...

Q: Let f(x,y) =x2-xy +y2-y. Find the directions u and the values of D,f(1,- 1) for which the following ...

A: Since you have asked multiple questions in a single request, we would be answering only the first qu...

Q: Use synthetic division and the Remainder Theorem to find the indicated function value: f(x) = x4 + 5...

A: We use the synthetic division method. The divisor x – 3 is in the form x – c, where c = 3. Arrange t...

Q: I multiplied two complex numbers in polar form by first multiplying the moduli and then multiplying ...

A:

Q: Find parametric equations for the lines in The line through (2, 3, 0) perpendicular to the vectors u...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Find the vertex, focus, and directrix of the parabola with the given equation, y2 - 4x - 10y + 21 = ...

A: first we will write it in the general form which is (y-h)2=4a(x-k) where (k, h) are the vertices sol...

Q: Evaluate 52 . 2 ?

A: we have to evaluate the given expression 52 . 2

Q: Graph the function ƒ(x) = 8 + 2x - x2 anddetermine the values of a and b that maximize the value of ...

A: Consider the function  ƒx=8+2x−x2  

Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

A:

Q: Determine the convergence or divergence

A: Consider the given series ∑n=1∞n2n4n3+1

Q: Find the domain of the rational function: g(x) = 2x2/(x - 2)(x + 6)

A: Given function is gx=2x2x-2x+6. Domain is the value for x for which function is defined. Here, given...

Q: On what the distance an object travels depend?

A: We know that the distance travelled by an object is given by  Distance=Speed × Time    Where  Distan...

Q: For the point with the given polar coordinates (4, 135°), determine the quadrant ________ in which t...

A: Let the polar coordinates be = r, θLet the rectangular coordinates be = x, yGiven that - r, θ = 4, 1...

Q: Minimize the function $f(x_1,x_2) = x^2_1+ x^2_2$ when subject to the constraint $x^4_1+ x^4_2$

A: Excessive symbols is creating confusion here. If possible please update with neat and proper questio...

Q: Find the total differential z = e−x tan y

A: we have to find the total differential of z = e−x tan y           dz=∂f∂xdx+∂f∂ydy        (1) where ...

Q: Calculating derivatives Find the derivative of the followingfunctions. y = ex(cos x + sin x)

A: Consider the given function, y=excosx+sinx use the product rule of the differentiation which states ...

Q: Find the maximum area of a rectangle that can be circum -scribed about a given rectangle with length...

A: the outer figure is a rectangle so, the angles will be the right angle     

Q: Find the exponential function y = Cekt that passes through the two given points.

A: here, y and t are the variables and the c and k are the constants the coordinates through which the ...

Q: Suppose lim

A: Given - limx→bf(x) = 7             ...............(1)limx→bg(x) = -3              .................(...

Q: Matching polar and Cartesian curves Cartesian and polar graphs of r = ƒ(θ) are given in the figures....

A: It is given that A sphere centered at  (a, b, c) with radius r is the set of points satisfying the ...

Q: Find the limit (if it exists). If it does not exist, explain why.

A: To evaluate the limit: lim△x→0-1x+△x-1x△x. Here, x will be treated as constant. When we put the give...

Q: The following figure shows the depth of water at the end of a boat dock. The depth is 6 feet at low ...

A: Given; y = A cos Bx + D 

Q: The graph of a quadratic function is given. Write the function’s equation, selecting from the follow...

A: The given graph is: