Consider the function f(x) - - 10 x² - 4 x7 Let F(x) be the antiderivative of f (x) with F (1) = 0. Then F(x)

Q: Use Pascal's Triangle to expand (4x² + 1)¹. Express your answer in simplest form.

A: The given expression .The aim is to expand the expression using Pascal's triangle.

Q: S²x²3x dx

A:

Q: The solution of the initial value problem dy/dx = y^(2) − 1, y(0) = 2 is an increasing function.…

A:

Q: Determine whether the Mean Value theorem can be applied t X + 5 [-6, 6] X-3 Yes, the Mean Value…

A:

Q: Find all vertical asymptotes of the following function. f(x) = 2x² 128 x² 17x + 72

A:

Q: If a = 37.7, what is O a. 2232.56 O b. 61.22 O c. 12.64 O d. 8934.23 O e. 4466.11 ["va² √a² = x²dx

A:

Q: Let f be a differentiable function such that f f(x) sec² x dx = f(x) tan x-f3x² tan x dx . Which of…

A: Consider

Q: 3. Let f(r) = 12z - 12 ³-²-4x+4' and let P/(r) be the partial fraction decomposition of f(x). (a)…

A:

Q: Find the particular solution. dy dx - 2y = 10, y = 4 when x = 0

A: Given , the differential equation, y = 4 when x=0We find the particular solution of the above…

Q: 5. An object moves along a coordinate line with velocity v(t) = 6t² - 6 units per second. Its…

A: We have to use the basic concept of definite integration.

Q: A particle moves along the y-axis so that at time t≥ 0 its position is given by y(t) = 3³-5t² +8t.…

A: The given position function is

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A:

Q: Consider the following acceleration a = a=9.8, v(0)=-11, s(0)=0 d's d1² initial velocity, and…

A:

Q: what is the addition or subtraction on formula used to write the expressions.

A:

Q: ff xdxdy where R is the region bounded by y = 0, y = 1, x = 2 and y=x

A: ∬xdxdyWhere R is the region bounded by y=0,y=1,x=2 and y=xy≤x≤20≤y≤1

Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and…

A:

Q: 1 six sided die is rolled twice. Let A be the event that the first roll shows a 3 and B be the event…

A:

Q: If f(1) = -5.4, f'(x) is continuous, and f₁ f'(x) dx = 20, what is the value of f(4)?

A:

Q: f f(x) = (sin²x)• (cos5x), evaluate f' TT 一 6

A: The given function is

Q: 2 x Find the volume of the solid generated by revolving about the x-axis the region under the curve…

A: To find the volume of the solid generated by revolving about the x-axis the region under the curve…

Q: Baby D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h' (c) = 0 ? Give a…

A: Let f(x) be th function f(x) is continuous on [a,b]f(x) is differential in (a,b) f(a)=f(b)Then there…

Q: If∫−15−97f(x)dx=15and ∫−15−97g(x)dx=11and ∫−15−97h(x)dx=25what does the following integral…

A: The objective of the question is to find the value of the integral ∫ from -15 to -97 of [5f(x) +…

Q: Determine each feature of the graph of the given function. f(x) Y = Answer Attempt 1 out of 2 −5x² +…

A:

Q: Find an equation for the tangent line to f(x) = xe²x at x = -1

A:

Q: Solve the exponential equations: A) e²x - 4ex - 5 = 0 B) 2x+¹= 3²x-1

A:

Q: How many permutations are there of 43 objects when taken 8 objects at a time, if a particular one of…

A: To determine the number of permutations of 43 objects when taken 8 objectsat a time if a particular…

Q: [1 0 1] Find the inverse of the matrix C = 0 1 1 using 2 1 4 cofactors. Show all your work.

A:

Q: Consider the following. f(x, y) = 8x 9y (a) Find f(7,4) and f(7.1, 4.05) and calculate Az. f(7,4)…

A: Consider the following.(a) To find .(b) By using the total differential   to approximate .

Q: Max is saving money to buy a new scooter. He decides to save $10 per week and starts with $50 in his…

A:

Q: Identify the inflection points and local maxima and minima of the function graphed to the right.…

A:

Q: Find the derivative of the following function. You do NOT need to simplify your answers. f(x) = e*…

A:

Q: Evaluate the following indefinite integrals: a. S 1 x²√36-x² - dx b. X -9 - 11-364 c. [²√²+² d.…

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

Q: Find the critical point of the function ƒ(x, y) = −4 + 4x + x² − 8y — 6y² - This critical point is…

A:

Q: The complement of an event E denoted E, is the event consisting of all outcomes that are not in E.…

A: According to probability theory, an event is a collection of potential events or outcomes also, we…

Q: 1 } [4ti 0 4ti +6t²j - 12 7K] (1+t) 4 k dtl

A:

Q: Given a-6, b-10 and y-120°, use the law of cosines find side c

A:

Q: For each value below, enter the number correct to four decimal places. Suppose an arrow is shot…

A: Suppose an arrow is shot upward on the moon with a velocity of 39 m/s, then its height in meters…

Q: Use the remainder theorem to find the remainder when f(x) is divided by x + 2. Then use the factor…

A:

Q: Determine the x-value of all critical points for the following function. f(x) = x-9 x² The…

A: To find the x-value of all critical points for the following function.

Q: The events E and F are mutually exclusive if their intersection is empty. Select one: O True O False

A: Given that E and F are mutulayy exclusive

Q: The population of a slowly growing bacterial colony after t hours is given by p(t) = 5t² + 20t +…

A: The population of a slowly growing bacterial colony after t hour is given byFind the rate of growth…

Q: Let f be a continuously differentiable function with f(3) = 8, f' (3) = 4. What is Xx f f(t) dt…

A: Let f be a continuously differentiable function with f(3)=8,f′(3)=4.L=limx→3∫3xf(t)dtf(x)−8∞∞…

Q: A four-digit PIN code is required for a bank's ATM card. An encrypted code is stored with the bank…

A:

Q: b. On what open intervals is f increasing or decreasing? c. At what points, if any, does fassume…

A: f'(x)=x(x-4)

Q: Find all possible functions with the given derivative. y' = 7+ 4

A:

Q: g (t) = = 3+t+t² √t

A:

Q: If A = (11) 01 " then eat = et tet et (& 0

A:

Q: Explore the Alternating Series Remainder. (-1)-1 K 2n-1 4 (a) Use a graphing utility to find the…

A: Given:

Q: (a) the function below. f(x) = 5√√√xe-* Find the interval on which f is increasing. (Enter your…

A: Increasing function : f'(x) &gt;0Decreasing function: f'(x)&lt;0

Q: 10 Find the derivative of: 4√ Type your answer without fractional or negative exponents. Use sqrt(x)…

A: Explaination of the answer is as follows