If f(t)= et and g(t) = 5t² - 2, use the chain rule to find the derivative of y = f(g(t)). y = est²-2. (10t) y' = e¹0t y = 10et et y=elot (5t² - 2)

Q: I ++ y + 22 Z 1) Consider the system of linear equations 3x 11. If we are using Cramer's Rule, we…

A:

Q: Let V₁, V₂. and v3 be vectors in a vector space V, and let T:V→→ R³ be a linear transformation for…

A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

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

A:

Q: Apply Green's Theorem to evaluate the integral. $(3y + x)dx + (y + 5x)dy C: The circle (x - 3)² +…

A:

Q: COLUMN A 17. To each person on the earth assign the number which corresponds to his age. 18. To each…

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

Q: dy Write down a differential equation of the form dt all other solutions diverge from y 9 as t →∞. =…

A: The differential equation has a form dydt=ay+b whose all other solutions diverge from y = 9 as t→∞

Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

A:

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: The function y = a. O a=3 O a = -2 ax4 +has a minimum at the point (√(√)). Determine the value of…

A:

Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) - 8 cos(0) = Enter your answer as a reduced…

A:

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: Consider the function f(x) = 3 - 3x², 3 - 3x², 4 ≤ x ≤ 1. The absolute maximum value is and this…

A:

Q: 10. [VF² dx [Vr³ dx 11. 12. [Vx¹0 de 13. (u²+u+1) du 14. dv / ( ²0¹² + √² + v) du [w³+²+ w dw 15. w3…

A:

Q: (y² + xy) dx-x² dy = 0, when x = 1, y = 1

A: Solution of given question is written in below steps.

Q: 3

A:

Q: Use integration by parts to find the following integral. 1 4x+5 dx X b 4x + 5 + Su dv = f dx. What…

A:

Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

A: To find equation of tangent line and then arc length of thegivencurve.

Q: 6 All open sets are bounded.

A: Some times true

Q: Consider the following. '6 dt Jo 36 + t² Let t = 6 tan(0) and determine the following.

A:

Q: Assume that x and y are both differentiable functions of t and are related by the equation y = cos…

A:

Q: Find a line that is parallel to the line that passes through both P and Q and contains R.

A: We have to find the equation of line.   According to our guidelines we can solve only one question…

Q: 1ln(1 + x) dx X 0

A: We have to integrate

Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

A:

Q: Please check the numbers again. You have used 3/8 in the above equation. Euqation is 3/2.   I…

A: ∫sec2u du = tan(u)+C

Q: Let f'(x)= = (x-1) (x-2)(x+1) and g'(x) = (x+2)(x-3) (x+3)

A: We have to find the interval in which f(x) and g(x) are decreasing.

Q: Kindly answer the question and provide a clear and correct solution. If I still get wrong…

A:

Q: dr 2√x+3+x d. ·S e. dx x√4x + 1 SIV f. dr x√4x²+1

A: These questions can be solved using integration by substitution.

Q: Solve the equation for z = C: i(z - 2i)² = 8 Select one: O a. z E-2, 3 + 4i O b. z € 2,-2 + 4i O C.…

A:

Q: What is the f(7) (-4) of g(x) = 2 205x53x¹ +9x³ +9² +2x+1 ? - 6 O 1/3 0 0 O-4 O 240

A:

Q: 8. Use the given graph to estimate the left Riemann sum for the given interval with the stated…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Consider the basis S - (V₁, V₂) for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the…

A:

Q: 비신부 4 x² sin(2x) dx

A:

Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

A:

Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

A:

Q: 4. Evaluate 12x+1 dx 5. Evaluate dx X 6. Evaluate [ 3x -¹ dx

A: To find the value of given integrals .

Q: 2 . show that V(x,y) = x 'f (2x+y) is the general Solution of: av X du 2X 1 = V ду dx

A: To show that, vx, y=x f2x+y is the general solution of: x∂v∂x-2x∂v∂y=v

Q: Find the volume of the given solid region bounded below by the cone z= sqrt(x^2+y^2) and sphere…

A: Here we have to find the volume of the solid region.

Q: Given the function y = f(x) defined at all real values of x. Let x = 2, 3, 5 and 7 are critical…

A:

Q: F Find the area of the region bounded by the curve y = x³ and the lines y = -x, y = 1. (Draw the…

A:

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

Q: Find the area inside one leaf of the rose: r = 5 sin(40)

A:

Q: The function y = a. O a=3 O a = -2 ax4 +has a minimum at the point (√(√)). Determine the value of…

A: Use derivative and find maximum or minimum value

Q: (b) the volume of the solid B that lies above the cone z = 3r² + 3y² and below the sphere x² + y² +…

A:

Q: he function f(x) - 2x³ 30x²+144x + 6 has one cal minimum and one local maximum. Use a graph of the…

A: Please refer to the image below

Q: Solve the given differential equation. All solutions should be found. dy e5x+10y = e dx NOTE: Use c…

A:

Q: dt 1³ +1²-2t

A:

Q: A rocket is fired vertically upward from the ground. The distances in feet that the rocket travels…

A:

Q: Evaluate the triple integral. [[[_xy sin(yz) dv, G where G is the rectangular box defined by the…

A: The given triple integral is evaluated below.

Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…