Let f(x, y) = 4x² + y². Using Lagrange Multipliers, how many critical points are there for f subject to the constraint equation x2 + y? = 4? (a) 2 (b) 3 (c) 4 (d) 5

Q: (d) lim sin x In x x→0+ (e) lim (sec x – tan x) x→T/2- x³ – 64 (f) lim x→4 x2 + 16

A:

Q: Evaluate log, 99

A: I am attaching image so that you understand each and every step.

Q: y" + 2y' + y = 7 + 75 sin 2x

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 40 ft/min, and its coarseness is such that ...

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

A:

Q: X-9 At what x- values is f(x) not differentiable?

A:

Q: Find the exact arc length of y 3 1 over [1, 2]. S 4х - +

A:

Q: Let F(x) = f(x) + g(x)e* + h(x)e²×+ C be the antiderivative of G(x) = (x+ e*), Determine the value o...

A:

Q: A solid E lies within the cylinder x2 + y2 = 1 below the plane z = 10, and above the paraboloid z = ...

A:

Q: Determine the surface area of the solid obtained by rotating y = V(2p – x)(2p + x), |x | < 2 about t...

A:

Q: In one of the warehouses of a construction firm, cement is being released from an elevated storage b...

A: Given: Cement is being released from an elevated storage bin at a rate of 29 feet3/min. i.e. The ce...

Q: x arctan xdx

A:

Q: 4 friends purchase an apple pie and a cherry pie to share. Each pie is $12. The 4 friends want to sp...

A: We need to choose correct option.

Q: Find the volume of the solid. y=x2, x=0; x=2, y=0, about the x-axis

A: use the volume of solid of revolution formula,

Q: Determine whether the geometric series is convergent or divergent. n=1 (-6)n - 1 O convergent diverg...

A: Let's find. 

Q: flying horizontally at an altitude of 1 mile and a speed of 480 mi/h passes directly over a radar st...

A: Topic:- application of derivatives

Q: Find the total area of the shaded region. The total area of the shaded region is (Simplify your answ...

A:

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. (1 - x)y' = y2

A: Firstly , Separate the variables and after that integrate . ∫yn dy = yn+1n+1+C . ∫1ax+b dx = 1a lna...

Q: 12w-5w2 +(20w-24) sec² (12w-5w )đw

A:

Q: Iff (x) is a polynomial with real coefficients and zeros of 4 (multiplicity 3), -5 (multiplicity 1),...

A:

Q: Using a calculator or computer, sketch the graph of f for k = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe ...

A: Given:     f(x) = e5x - kx    k = 1/9 , 1/6 , 1/3 , 1/2 , 1 , 2 , 4

Q: 6. DETAILS BERRAPCALC7 3.6.025. 0/2 Submissions Used For the equation, find dy/dx evaluated at the g...

A: We will find the implicit differentiation at a point. 

Q: A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on t...

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 4t, y = 4 –...

A:

Q: 3. Find g if g'(x) = 8x(x® – }) and g(2) = 3. %3D %3D

A: We will find g. 

Q: Which of the following correctly changes the integral rdrde from polar coordinates to rectangular co...

A:

Q: [17(xe" +e* )sin(xe*)-14sin(x)dx

A:

Q: Give two other polar coordinate representations of the point, one with r 0. (r, 0) = ( 3, – 2.14 X ...

A:

Q: + - -5 8 23)+(1,4)

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist, ...

A:

Q: 18) Find a + b, 2a + 3b, |a|,  and |a - b|.  a = 2i - 4j + 4k, b = 2j - k

A: The objective is to Find a + b, 2a + 3b, |a|, and |a - b|.

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

A: We have to find the critical point

Q: Let f(x, y, z) = 6xy- z, x = 3r cos(0), y = cos (0), z = 3r. = . Use the Chain Rule to calculate the...

A: fx,y,z=6xy-z2x=3r cosθy=cos2θz=3r

Q: Use areas to evaluate the integral f(x) = 3x + 9-x on the following intervals. (a) (-3,0] (b) [-3,3]...

A:

Q: Sketch the region bounded by the given curves and find its centroid

A:

Q: x=t +1, y=r -t c) Find an equation of the tangent to the curve at the point corresponding to t = 1. ...

A:

Q: what is the domain and range of: f(x) = √x −ln(x).

A:

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(2, 8...

A: Formula to find directional derivative of the function F at a point P(x,y,z) in the of a unit vector...

Q: Give two Partial Variation example problems and their solutions.

A: It is required to give  two Partial Variation example problems and their solutions. It is known that...

Q: The vector v and its initial point are given. Find the terminal point. = (4, -9); Initial point: (9,...

A: Given

Q: Evaluate the integral i- te*j + VTk] dt 0,

A: ∫03t2i - tet2j + t7/2k dt [t3i/3 - et2j/2 + 2t9/2k/9 ]03 9i - e9j/2 + 2*35/2k (9 , -e9/2 , 235 )

Q: Consider the equation and the given point. f(x) = (x - 3)(x? + 6), (1, -14) (a) Find an equation of ...

A:  

Q: Prove the identity. (Recall sinh(a + b) = sinh(a) cosh(b) + cosh(a) sinh(b).) sinh(2x) = 2 sinh(x) c...

A:

Q: In a local art museum, a moving spotlight projects geometric figures on the wall in front of it. The...

A:

Q: The winner of a "million dollar" lottery is to receive $50,000 plus $50,000 at the end of each year ...

A:

Q: dy 21 z'e ", by using Variable Separable de PROBLEM [ B6 (b) ]: Solve the first order differential e...

A: Given the first order differential equation is dydx = 21x2e-y

Q: b.y = x100 ; find dx100 d'100y (100th derivatives)

A:

Q: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, + (...

A:

Q: The velocity of a car is f(t) = 5t meters/second. Use a graph of f(t) to find the exact distance tra...

A:

Q: A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base ...

A: Here we have to use the application of derivatives