2. +4y= sin(3t), y(0)=2, y'(0) = 0

Q: Find the slope of the tangent line to the graph of the given function at the given value of x. 1/2…

A: We want to find slope at the point x=25

Q: Question 4 A conical water tank has its top at ground level (consider this to be the x-axis) and its…

A: The given problem is solved below in detail.

Q: Problem 7 x√x + 1 dx

A: Given ∫07xx+13dx

Q: 4. 2x3ý = y (y² + 3x²)

A: The given differential equation is  2x3y'=y(y2+3x2).

Q: R is the region bounded by the functions f(x) = -7 and g(x) = -4x - 10 over the interval [a, b]…

A: We have to find the integral

Q: The value V of a machine t years after it is purchased is inversely proportional to the square root…

A:

Q: 1. Evaluate the integral: (a-1/3 - 2/3) da X

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…

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

A:

Q: Derive the following function 1 1. v = x²√x + √²²³√x 2. g(r) = (r²2r)er

A:

Q: B. Find the general solution of the following 2nd order differential equation: y +2y + 2y = 0

A: To find the general solution of the following 2nd order differential equation.y''+2y'+2y=0

Q: Using Fundamental Theorem of Calculus (FTC). Compute the following

A:

Q: 6. Find of z = In(xy) 8²y

A: Given:       z=lnxy     ∂z∂y=∂∂ylnxy  Treat x as constant  Apply chain rule:…

Q: :S- 8x + 1 √4x-3 dx. If we let the substitution "=√√4x-5, the resulting integral Given : becomes Ⓒ =…

A: The integration of the integral is (8x+1)sqrt(4x-3).

Q: A biochemist is testing the effect of a new antibiotic on a particular mould growing in a petri…

A: We need to find time and rate of area increase. As per Bartleby's guidelines we can only solve 3…

Q: Find the altitude of a rectangular closed box with volume 100 cubic inches with length twice the…

A:

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: We need to choose correct option.

Q: A conical water tank has its top at ground level (consider this to be the x-axis) and its base 12 ft…

A: Let's find total work(W).

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: We can solve the given question as below.

Q: 4. 2x³y = y (g2 + 3z2)

A:

Q: Q1:Discussion a continuity of the function f(x, y) at the point (0,0), where ey sinx f(x, y) = X (x,…

A: We want to check the continuity of the function at (0,0)

Q: FCILICI B. Find the general solution of the following 2nd order differential equation: y +2y + 2y =…

A:

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

A: Thr solution is given in the next steps.

Q: Evaluate (x+2√Y) ds where C is given in the accompanying figure. (x+2√y) ds =D (Type an exact…

A:

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

A:

Q: Calculate the inverse Laplace of: (s-1)e-2 s²+8s +13 ^{²

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: Σαβη (117)

A:

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

A:

Q: 2 [² fo Given f(x,y) = x²y-3xy³. Evaluate fdy

A:

Q: Question 14 A 60-m climbing rope is hanging over the side of a tall cliff. How much work is…

A:

Q: For the given function f(x,y)=x²y³+3x³y, find a flay

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: Find the transition points. y = 3x² - 42x6 (Use symbolic notation and fractions where needed. Give…

A:

Q: In pair, study and find the integral of the following functions. You will be awarded marks for each…

A:

Q: Q2: A. Determine if p=i-3k and q = 61 - 3j - 4k are parallel, orthogonal or neither.

A: According to Bartleby guidelines I can only answer the first question of the two questions given.…

Q: A man 5ft tall is walking along a straight line at a rate of 3ft/s towards a lamp post that is 15ft…

A:

Q: test if (AB) =B¹A¹ A = 4 0 L3 1 2, B = 5. 4 -3 14 02

A: We  can check the matrix as below

Q: Question 5 What is the amount of work done on a spring when it is compressed from its natural length…

A:

Q: (x²-1) + 2y = (x + 1)² dy dx

A:

Q: 1. Lim x-2 X x² - 4 x³ -x-6

A: Lets factor x3-x-6: x3-x-6=x3-2x2+2x2-4x+3x-6                =x2(x-2)+2x(x-2)+3(x-2)…

Q: Find ² of 2 = 2x³ - 5xy² z xy

A:

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

A:

Q: If A = 2₁ 2 2 and B = -1 Find det(AB) 3

A:

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: f(x)-f(a) a. Use the definition mtan = lim x-a x→a b. Determine an equation of the tangent line at…

A:

Q: iv) in complex number z³. (z)² = |z|².z

A:

Q: Evaluate the following: π 1.² (cot 20 + csc 20) de 6 TU cost 2. S1-sint 2 dt

A:

Q: Suppose f'(2)=6 and g'(2) = 9. Find h' (2) where h(x) = 4f(x) + 3g(x) + 6. h'(2)=

A: Topic = Derivative

Q: What is the amount of work done on a spring when it is compressed from its natural length of 1 meter…

A: Compress from the natural length through 1-0.8= 0.2 meter spring constant 'k'=16 N/m

Q: (c) Show that the function is a solution of the differential equation (−1)" x2n f(x) = Σ (2n)! n=0…

A: