6. Given the function ƒ (x) = x² + x − 3, find f (x + 1). 7. h(x) = 2x+ 1, find h(3) 1 8. Given f (x) = 1, find f(-5).

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

A:

Q: 2. Find the root of the function/ (Take the tolerance as 0.01) 4 by using the Newton-Raphson Method.

A: The given problem is to find the approximate root of given function using the Newton raphson method…

Q: Find the Inverse Fourier transform of Te-lw||

A:

Q: Q5. Check whether the given points A (1, 2, 3), B (3, -1, 4) and C (-2, 3, -4) are collinear.

A: If there points A,B,C are co linear then we can have  |AB|+|AC|=|BC| . (A,B,C may have interchanged…

Q: 1: Which of the following vectors are linearly dependent? 21 1 2 A: -4 and L C: 0 B: 2 and 4 [3] [6]…

A: We know that definition of linearly dependent vectors ,  A set of vectors is linearly dependent if…

Q: Consider the figure below. (Use the rules for working with measurements to give your answers to the…

A: We need to point only the rectangular sides and not the triangular sides

Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

A:

Q: Q4) Use the Newton- Raphson method, with 1.5 as starting point, to find solution of f(x)= x-2sinx.

A:

Q: 3. Determine the center and radius of the following sphere: x² + y² + z² - 2x - 4y + 8z - 15 = 0

A:

Q: y = -0.2 (x−5) -6

A: Consider a function y=0.2x ......(1) The graph of the function is

Q: Q1) Evaluate the following integral by using Odd and Even Powers Method: y = cos(x) dx

A:

Q: 1 It is given that p(x) = x³ + ax² + bx-48. When p(x) is divided by x-3 the remainder is 6. Given…

A:

Q: Q1:/ Read the article below and answer the questions after. PM25 is the leading global environmental…

A: By using sentence mentioned in given paragraph i.e., PM2.5 is the leading global environmental…

Q: Find the area of the surface generated when the curve f(x) = 9 tanx on [] Area = (Type an integer or…

A:

Q: The population of a small country by year is shown in the table below. Year 1960 1955 284496…

A: As per our guidelines we will answer first 3 subpart. Kindly repost other questions.

Q: I Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z…

A: Let E be solid inside the surface x2+y2+z2=25  that lies above the surface z=3x2+3y2 . To Find and…

Q: 7: The point X* = [00] for the function f(x) = 2x² + x² + 2 represents a A: Saddle Point for f(x) B:…

A: Given :  f(X) = 2x12+x22+2,  for  X = (x1 , x2) To find : We to check the nature of point  X* = (0,…

Q: O Consider the following matrices 0 ^- (-¹2 ~) -- († ;) -- (1 ¹/² : ;) -- (:) --( : ) 1/2 3 A = D= 1…

A: We will use property of matrix multiplication  Two matrix can be multiplied only when number of…

Q: (1) Jacob graduated from Harvard university graduation, (Jacob has been in the US. for five it is…

A: These are from Logic.

Q: what is the difference between Binet's formula to its simplified version? Are there any rules on…

A:

Q: marks. THE CO igle in 111° 103° 122 polygon all of ning for

A: We know that sum of all angle of pentagon = 540 And 4 angle is given 122, 103, 111,90 and let assume…

Q: x³y" + xy' - y = 0 ; y=x

A:

Q: The polar equation r(0) = 4 + 5. sin(0) is graphed below. 15- 14 13- 12 11 10- 9 8 7 6 5 O 4 3 2 10…

A: Please see the type syntax

Q: Which type of speech parts, the below words belong to? Show the part of speech with more details,…

A:

Q: Q₁. A: Find x²dx by using Riemann integral. √x=0 Q, B: Let f' be a continuous function on [a, b].…

A: Lets solve both questions

Q: Let be the double integral given by -22 0 (4-(y-2) dxdy, do the following a) draw the region of…

A:

Q: If u and v are the two solutions of d'y dy dx² + P + Qy = 0 dx uv₂u₂v + P (uv₁ - u₁v) = 0 (uv₁u₁v) =…

A: The given differential equation is d2ydx2+Pdydx+Qy=0.....(1) To prove: (a) uv2-u2v+Puv1-u1v=0…

Q: [3] Determine the area of the triangle determined by the polar point (18, 240").

A:

Q: solve by using Laplace Transform y"-10y'+9y=5t, y(0)=-1, y'(0)=2

A: Use Laplace table.

Q: nies that sell identical products. Company 1 ca 27. Meanwhile, Company 2 can sell the produ off…

A: Game Theory is the study of decision making strategies of two individuals or agents where their…

Q: 5. Find the slope for f(x, y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: To find the slope for function f at point P in the direction of the line from M to N.

Q: For the graph below, find an Euler circuit in the graph or explain why the graph does not have an…

A: To find- For the graph below, find an Euler circuit in the graph or explain why the graph does not…

Q: - What is the second derivative of the function f(x) = xex ? What is the coefficient of the third…

A: solution is given below:

Q: (a) Given functions f(x) = 3x +2 and g(x) = x3³ - 1, find fog and the inverse of fog. 4. (b) Use the…

A: To solve the given problems :-

Q: 8: What are the values of kER for which the function f(X) = -2kx² + x₁x² + 4x will have a strict…

A:

Q: 1. Find the Fourier series of the function f(x) = |x| which is defined over the range - T<x< T.

A: f(x) is periodic with period 2π  f(x) is continuous except at the end poits (where f is not defined)…

Q: 1 2 If R = 3 1 that R² = 2R + cS. and S= 1 1 0 0 1 find a number c such

A: Solving matrices question by finding square of R matrix

Q: 6. The matrix P = has eigenvector general solution of the system ' = Px. with corresponding…

A:

Q: 15 Down: The ODE in r we must solve when solving the vibrating circular membrane is due to ________

A: To slove the puzzle

Q: Fill in the table and sketch the graph of the following equation. f(x) = -2x - 5 3x + 18 =

A: The given function is f(x)=-2x-53x+18.

Q: For which real numbers k is the matrix [3] k -31 A: k> 3 B: k=3 C: k <3 3 positive definite matrix?…

A:

Q: (i) Use the chain rule to show that -3x = (In 3)32 dx Hint: use the fact that 3 = eln 3ª (ii) Use…

A:

Q: . Use x,  y and z as variables to rewrite the following sentences to mathematical statements  A…

A:

Q: 19 1. The expression -1 n is equal to n=1 9 O 45 O 50 O 362880

A: I have given the answer in the next step. Hope you understand that

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

A:

Q: 9: In the steepest descent method the vectors (Xk+1-Xk) and (Xk+2 - Xk+1) [2 [4] 2 are orthogonal…

A:

Q: Borderland and are now asked by the game m Arisu must decide between the light and dar el and demon…

A: "Nash equilibrium is computed from a payoff matrix which represents the payoffs of each players from…

Q: 5. Interest rate. A 2-year loan of $4650.25 accumulated $269.75 in simple interest. Calculate the…

A:

Q: (A) Find the general solution to ONLY ONE of the following differential f ations (1) (sec(y))² y' -…

A: We solve the given ODE  (sec(y))2y'-3tan(y)=-1 ......(1)

Q: Find arc length: r(t) = 3 cos ti + 3 sin tj + 5tzk

A: