A quadratic function f is given. f(x) = 4x² + 8x + 5 (a) Express fin standard form. f(x) = (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.) (x, y) = vertex x-intercept (x, y) = y-intercept (x, y) = (c) Sketch a graph of f.

Q: Given that Vƒ(2, −11) = 6 i – 3j, find the directional derivative of the function ƒ at the point…

A:

Q: The two open disks B((1, 2); 2) and B((-2, 1); 2) has intersection. True False

A:

Q: Evaluate the integrals. Making use trigonometric Substitutions. dx (a^² + x²³²) ³/2₂ St

A: The given integral is 1/(a2+x2)3/2. Repost the next questions.

Q: Answer parts (a)-(e) for the function shown below. f(x)=x³ - 2x²-x+2 a. Use the leading coefficient…

A:

Q: Assume that x and y are both differentiable functions of t. Find the required values of and dy dt…

A:

Q: For the given function, find all as f(x) = 2 Ex 7x² + 12x - 4 +1

A:

Q: Suppose that (g(x))² + 5x = x²g(x) + 15, and that g(2) = 5. Find g'(2).

A:

Q: c) fsin-¹(x) dx -1

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: 5. We know 6+ i and 4-√3 are roots of a 4th degree polynomial. Find the remaining roots.

A:

Q: Consider the function f(x) = S|1-x²| cos(x) x ≤ 0 x>0 (a) Evaluate the function at x=2. Enter your…

A: The given function fx=1-x2x≤0cosπ2xx>0 We have to sketch the graph of the function and find the…

Q: If f is continuous for all nonzero z and y, and f(0,0) = 0, then f(x, y) = 0. lim (z.g)-(0,0) True…

A: Given query is to find statment is true or  false.

Q: Solve the ff. first order DE using Separation of Variables 2 b. x²dx + y(x − 1)dy = 0

A:

Q: In Exercises, solve for y in terms of t or x, as appropriate.51. ln (y - b) = 5t                52.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 28. (1+x¹) dy + x(1 + 4y²) dx = 0, y(1) = 0

A:

Q: Match each function f with a function g so that (fog)(x) = x². (x² + 2)² (²-2)² x² - 2x + 1 :: 2 ln…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Next Find the maximum and minimum values of f(x, y, z) = 3x + 2y + 4z subject to the constraint +2y²…

A:

Q: The population of Silver Run in the year1890 was 6250. Assume the population increased at a rate…

A: Given: Initial population in 1890:  P0=6250 Growth rate: r=2.75%   (a) To estimate the population in…

Q: Solve the ff. Linear Equation: 33 a. (x³y³ + 1)dx + x³y² dy = 0

A:

Q: i got -2 square root of 5 and positive 2 square root of 5

A: We shall use Lagrange method for find maxima and minima Let lambda be any real number We find lamda…

Q: 1. v and w are two non-parallel vectors. If 2v-3w and v-(x-1)w are parallel vectors, find the value…

A:

Q: 2. y = ln 3. y = 1+sinx 1–sinx e3x-e-3x e3x+e-3x (use properties of logarithms)

A:

Q: Solve the ff. first order DE using Homogenous Equations. b. (x - 2y)dx + (2x + y) = 0

A: We have to find the solution.

Q: 1. Compute the three partial derivatives of f(x, y, z) 1 (x² + y² +2²)n

A: see below the answer and calculation

Q: Use implicit differentiation to find az/ax and əz/ay. xy²z³ + x³y²z = x+y+z

A:

Q: Find the directional derivative of f at the point P in the direction of a. a=i-j NOTE: Enter the…

A:

Q: PLOT THE GRAPH FOR THE GIVEN CURVES AND CONDITIONS BELOW Need to find out the differential equation…

A:

Q: f (s, t) = S s² + 1²

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

Q: Evaluate the integral: x = 49 tan (0) 49 sec (0) F 0x = 30x² - dx (A) Which trig substitution is…

A:

Q: Calculus Find the radius of convergence for the series (2n)! (n!)2x¹.

A: ∑n=1∞ 2n!n!2xn

Q: a. In 25-In 64 +In 27 3

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

Q: Suppose that (g(x))² + 8x = x² g(x) + 4, 2 and that g(3) = 4. Find g' (3).

A: Given query is to find indicated derivative.

Q: Find the limit lim h+0 f(−11+ h) − f(−11) h ‚ if f(x) = √1069 – 6x².

A:

Q: If f(x) = (4x² + 5)5/2, compute the first and the second derivative of f(x). f'(x) = f"(x) =

A: Given query is to find first and second derivative.

Q: 1. Find the extrema and/or the saddle points of the functions. a) f(x,y) = e4y=x²-y² b) f(x, y) = (1…

A: Note:sorry for the  we should solve only one question , as solution is too long. Hence please repost…

Q: Problem

A:

Q: Solve the following differential equation using Laplace d²x dt² 2 dx +2+x=1 x(0)=x'(0)=0 dt

A:

Q: a. xy³ dx + (y + 1)e¯*dy = 0

A: xy3dx+y+1e-xdy=0

Q: lim X->15 x+10 5 x-15 c/+X

A:

Q: Express the ratios in Exercises 69 and 70 as ratios of natural loga- rithms and simplify. log,a log2…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Let f(x) = x (f+g)(5) + 2 and g(x)=x²-x. Find and simplify the expression. (f+g)(5)= (Simplify your…

A: we need to find (f+g)(5).

Q: Use a contour map of f(x, y). 4. 2. 0 -2 7 -20 B B C O A -10 70 50 30 LLL 10 0. 10 C -30 -10 2 .30…

A: Given a contour map with value of each component as A=30, B= 20, C=-10 for f(x,y) We have to choose…

Q: A thermometer is taken from a room where the temperature is 23°C to the outdoors, where the…

A: Explained below

Q: Find the arc length of 2 + 3/2 from x = 1to x = 4.

A:

Q: 7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where F2…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: lim 60 SiA (-78) (10

A:

Q: 4x² 1. Let y=f(x) = 4x+1

A:

Q: ← Graph the feasible region for the system of inequalities. Tell whether the region is bounded or…

A:

Q: f(x)= 9x x2+8x + 15 Vertical asymptotes: x= -3, x=-5; Horizontal asymptote: y = Vertical asymptotes:…

A: Topic:- application of derivatives and calculus

Q: Eliminate the Arbitrary Constant in the ff. equations: 3 a. x - 2 3x y = C

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