Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E R. . Show that the curve C has a horizontal tangent line at the point (0, -9). . Evaluate the second derivative at the point (0, -9). d²y dx²

Q: Find the market equilibrium point for the following equations: Supply: .10x + 5 Demand: -.15x + 10

A:

Q: Find the y-intercept of a quadratic function containing the following points: (2,5), (1,0), and (-2,…

A: Topic:- function

Q: Differentiate y = √x + √z 01 O 2√x+1 A+ 2√x + 2√x O 2√x + √x

A:

Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

A:

Q: = f(x) = ='(x) = L'ea 1 t²dt then

A:

Q: This exercise uses the population growth model. It is observed that a certain bacteria culture has a…

A:

Q: 3. Find the domain of f(x) = 1- 1 X X

A: We have to find the domain of f(x)

Q: What is the slope of a line that is perpendicular to y = 3x + 1? -1/3 -3 3 1/3

A:

Q: Type the left side of the equation of the ellipse. Which graph shown below is the graph of the…

A: Topic:- geometry

Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d da 12 to dt =

A:

Q: y (az + √2) sin (ay²) dy + (az − √√2) dz = 0 4√2 ln az + √2 = C 4√2 In az + √2 = C 4√2ln az + √2 = C…

A:

Q: `11,  Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence,…

A: The solution is given below

Q: The infinite series Σ a. series liner 8 n¯4 is a

A: We know that the p-series is the following. Thus, for             p=4.

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: If z = tan X 2 then sin x =

A:

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: Consider the function f(x) = = Let F(x) be the antiderivative Then F(x) = 7 3 x² x7 of f(x) with…

A:

Q: If what does the following integral equal? [q(w)dw = [ [²³q(w)dw = 12 and q(w)dw = 9.4 1. 2

A: This question can be solved using the concept of definite integrals.

Q: decimal places. a) 3tan x an(x - TU 5 +4=6

A:

Q: Consider points P(-1, 3), Q(1, 5), and R(-2, 8). (a) Determine vector PQ and express it in component…

A:

Q: Find the solution to ty""+612 y" +29ty-29y=0; y(1)=2, y'(1)=-3, y"(1)=19

A: The given equation is; t3y''' +6t2y'' +29ty' -29y=0, y(1)=2, y'(1)=-3, y''(1)=19.

Q: 1. Consider the region R bounded by the functions f(x)=3x and g(x)=x²+2. The centroid of R is: a.…

A:

Q: Given f(x) = x² + 2x-5 and values of the linear function g(x) in the table, what is the range of (f+…

A:

Q: [₁₁ ) If nd f*. f(x) dx = 4 and g(x) dx = 1, what is the value of ولاء f(x)g(y) dA where D is the…

A:

Q: (b) Show that the following sequence is convergent: 1+ (-1)" n² Yn = √2+ (c) Show that (yn)neN is…

A: A Sequence <an> is convergent if and only if limn→∞ an is finite and unique.

Q: Consider the function on the interval (0, 27). sin(x) f(x) 4 + (cos(x))² (a) Find the open intervals…

A: Find out the intervals on which the function is increasing or decreasing and also find out the…

Q: Find the limit and determine if the function is continuous at the point being approached.

A: This question can be solved using the concept of limit and continuity.

Q: a=, b= a) a-2b b) a + b c) à b d) The angle between a and b =) Find all vectors which are twice as…

A: We need to solve vector problem..

Q: 1/3 0 4x dx √25-x

A: Given Problem:- ∫0134x25-x4dx

Q: an List the first five terms of the sequence. 1 + an a₁ 1 a2 23 a 4 25 || = = = a1 = 3, = an+1 =

A:

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: 5. S (2x²+1) x3-3x+2 dx

A: Here we have to find the integral.

Q: Evaluate: fre Hint: Use dyda as order of integration. ezz drdy

A:

Q: Suppose that P = f(t) is the population (in millions) of the country t years after the year 2000.…

A: Given that P= f(t) is the population (in millions) of the country t years after the year 2000

Q: 1 3 2 + To find the blue shaded area above, we would calculate: b ľ f(x) dx = area Where: a = 2 3 4…

A:

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

A:

Q: Using polar coordinates, evaluate the integral Se sin(x² + y²)dA where R is the region 4 ≤ x² + y² ≤…

A:

Q: Find equations of all tangents to the curve f(x) = 4/x that have slope -1. Options attatched

A: f(x) = 4/x                    Slope of tangent = -1

Q: 3. Find the domain of f(x) = = 1 - 1- x X

A:

Q: Consider the two-dimensional vectors a and b. a = (3,-1), b = (-5, 0). (a) Find the measure of the…

A:

Q: sigma 4-0 (1-x)/sqaurerootx dx

A:

Q: The graph of a function f is given. Use the graph to estimate the following. local maximum local…

A: Please see the below picture for detailed solution.

Q: Consider points P(-1, 3), Q(1, 7), and R(-4, 9). (a) Determine the unit vector in the direction of…

A: The objective is to determine unit vector in standard form and as well as component form.

Q: Using polar coordinates, evaluate the integral // sin(x² + y²)dA where R is the region 4 ≤ x² + y² ≤…

A: Concept: Dual integrals in polar space: An iterated integral in polar coordinates can be used to…

Q: Using the Factor Theorem, which polynomial function has the zeros 5 and 4-5/? Ox²-9x-5x + 25/+20…

A:

Q: 2 8 X2 x4 + x2 dx

A: To solve the given integral.

Q: Express the limit lim n→∞ a = n b = i=1 Provide a, b and f(x) in the expression (6 cos² (2πx)+5) Ax;…

A: To find value of a, b and f(x).

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

A:

Q: Find the volume V of the solid of revolution that results when the region under the graph of f(x) =…

A:

Q: Find an equation for the hyperbola described. Graph the equation Center at (-1,-4); focus at…

A: