2. f x cos² x dx

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: Find the indefinite integral: A X+X+C B x³ + x² + c с x5/5 + x²/2+c D 5x5+2x²+c Sx(x³ + 1)dx

A:

Q: 3. The angle between vectors A = 91-j+5k and B=(-2,7,1) is... ***** 16- 12 4. 2) shor mis

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

Q: Simplify to an expression involving a single trigonometric function. Please show work so i can…

A: SOLUTION-

Q: : Evaluate the following integrate: 1- S x²dx √9-x² 2-√(2 + 5x) e dx

A:

Q: Q2. Find the exponential Fourier series for f(t): (1 = Fourier series. 0<t<1 (2 1<t<2 then find the…

A:

Q: Determine the values of m and b such that function g is continuous at every real number: if r 1.

A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

Q: Q4:Evaluate 1) lim (1-²) x-0 \sin x

A:

Q: Consider the function f(x) = 2 - 7x², −4≤ x ≤ 1. - The absolute maximum value is and this occurs at…

A:

Q: Find the slope of the tangent line to r²e³ + y²e² = 2e at (1,1).

A:

Q: Derive the formula for trapezoidal Rule to evaluate f f(x) dx

A: The trapezoidal rule is to find the exact value of a definite integral using a numerical method.

Q: B. The vector =(4,-2, 1) ends at the point P=(7,-7,2). At what point does the vector start?

A: Note: Here, question A is an initial value problem (IVP) but initial values are not given.Therefore,…

Q: Rewrite the Cartesian equation y = r(0) = = Enter theta for 0 if needed. 2x² as a polar equation.

A: In this question, we need to convert the given cartesian equation to polar equation.

Q: 6. (10 points) Give the equation of the tangent line of the following function at point a = 1: xe…

A: Solve by Differentiation

Q: 19 A curve with polar equation r = 8 sin 0+17 cos 0 represents a line. This line has a Cartesian…

A:

Q: a. The object's velocity after 5 seconds is (Round to the nearest tenth as needed.) m/sec.

A: We have to find the velocity after 5 sec

Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: 1. (ex + lny + 7) dx + ( 85 + In x + siny) dy = 0

A:

Q: ?T f(t)=√ t` cosnt dt ((나) ans = 4 12 The easiest way to solve the integral so that the result is as…

A:

Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

A:

Q: Find the slope of the tangent line to the curve - 4x² + 4xy - 1y³ = - 148 at the point (3, 4).

A:

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: -1 (a) cos (b) log5 (25) -√√3 2

A: Solved below.

Q: 2 Find all local extreme values of f(x) x³ + 11x²56x + 30. = 3 The FIRST local extreme value, moving…

A:

Q: If = (-12, 4, 8) the position vector of u is......

A:

Q: tan² y = x (By implicit differentiation)

A: The given equation is tan2y=x.

Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.

Q: Derive the following function 9. y In x+1 x-2 10. Dºsin(x)

A:

Q: Question C.) - hit In n 231 n

A: We have to find the series coverges

Q: Function Point f(x) = tan² x 4 (a) Find an equation of the tangent line to the graph of -4x-T+1 X…

A:

Q: 1. Prove that (a) A\B=A\(ANB) (b) A\(B\C) = (A\B)U(ANC) (A\B)\C=A\(BUC) (c)

A:

Q: Given f(x,y) = ex cos y, Evaluate f,(0,2) (A) -sin 2 B) 0 C) e² D cos 2

A:

Q: y = x^ (Hint: First take LN of both sides and use implicit differentiation.)

A:

Q: Given f(x,y) = x²y-3xy³. Evaluate 2 S₁² 0 fdx

A: Follow the procedure given below.

Q: Find the length of the arc of a circle of diameter 10meters subtended by a central angle of π/4…

A: Given:  diameter =10meters

Q: y = sin² (3x)

A: Topic = Derivative

Q: Fill in the blanks in the following: 1. Ifa (3,-2, 6) and b=(4,-1,-6) the axb:

A:

Q: da potential function f for the field F. F = (4y + 2z)i + (4x+z)j + (2x+y)k eneral expression for…

A: Topic:- application of integration

Q: 14. √ √2-√x dx

A:

Q: 1 2. Lim x0x 1 sin x

A: Given:      limx→0+1x-1sinx simplifying we get     =limx→0+sinx-xxsinx Apply L'Hospital's Rule:…

Q: Find the transition points. y = 15x³ + 360x² (Use symbolic notation and fractions where needed. Give…

A:

Q: Find the dimensions of the largest rectangle that can be inscribed in an isosceles triangle if one…

A: We need to find dimension of rectangle.

Q: The graph of f is given. y 3 * X -4 2 (b) What are the domain and range of f−1? (Enter your answers…

A:

Q: The region in the first quadrant bounded by the graph of y=8-x32, the x-axis, and the y-axis is…

A:

Q: Evaluate Th - dx ¹1+x

A:

Q: Make Detailed solution INTEGRATION OF TRIGONOMETRIC FUNCTIONS

A:

Q: X -dx 3. Using a suitable change of variables, determine the indefinite integral: √1 x² [ (sin² x)…

A:

Q: The graph below is the function f(x) 5+ 4 -5 -4 -3 -2 -1 1 2 3 4 Find lim Find lim Find lim Find…

A: