Exercise 14.5.1 dz for the the following functions To calculate z = f(x, y) = 2 – 3ry + 2y? I = r(t) = 3 sin 2t, y = y(t) = 4 cos 2t %3| first calculate: dz az dy dz dy dt Then use the formula above to find the derivative in terms of r, y, and t: dz dt Finally, substitute expressions for z and y to write the final answer in terms of t: dt

Q: Refer to the figure below to find the limit lim f(x). X - 00 3.5- 2.5- 1.5- 1- 0.5- 2.

A:

Q: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

A: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

Q: Write a in the form a = a-T+a,N at the given value of t without finding Tand N. r(t) = (3e'cos t)i+…

A:

Q: If f(x) = v4x + 1 find f"(2). %3D

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

Q: Please Attach the Venn Diagram of the given problem including the complete solutions to answer the…

A:

Q: 2 v2x-x2 XY xydydx 0 0

A:

Q: 6. Use Newton's method to find the third approximation to the root of: x* + 2x – 4 = 0. Use x,= 1 as…

A:

Q: As x approaches 5 the value of 2x+ 8 approaches

A: Substitute the value of x in the given equation.

Q: Let -1 <a < 1, the series r na" is the power series representation of the n-1 function Select one:…

A:

Q: Use the graph to find the following limits and function value for each value of a. i) lim f(x) i)…

A: Given query is to find indicated limits.

Q: 3

A: We will find the limit.

Q: 2 | [ cos ti- sin 7t j+sin 6t k]

A: Given :

Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

Q: Evaluate the integral |- 5x + x3 - 2 x5 dx 3

A: Topic:- integration

Q: 1 erivative of x²+2

A:

Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

A:

Q: Find the vertical and horizontal asymptotes. (Enter your answers as comma-separated lists of…

A:

Q: dy Find by implicit differentiation dx 4 + 5x = sin(xy*) dy dx II

A:

Q: Write a in the form a = a-T+aNN at the given value of t without finding T and N. 3 (5 e'V5)i+…

A:

Q: Evaluate dx -31 x a,

A:

Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: Use l hospital rule for finding the limit.

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that3 + x – 1 =0 has exactly one real…

A:

Q: 3. Determine the balance A for $7,000 invested at a rate of 4.5% for 20 years, compounded a. Monthly…

A:

Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

A: We have to find the points and check the nature of function.

Q: Find the Taylor series of  f(x)=ln(2+x) around the point x=-1 by reaching the term n=4

A:

Q: Find the general solution of the differential equation. (Use C for the constant of Integration.) dy…

A:

Q: 1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y]…

A:

Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

A:

Q: Let R be the region of the 1st quadrant enclosed by x=y^2 , x=2-y^2 ,y=0 . 1.1 Draw an area R.…

A: Given that;  x = y^2   and x = 2 - y^2       Let's find area between two curve in 1st quadrant.

Q: r(10,3,3) dx (1,1,1) dy dz. - -

A:

Q: ven the function f(x) = -x* – 4x termine its critical points and assify then, determine the point(s)…

A: Topic:- calculus

Q: Find the volume of liquid needed to filla sphere of radius R to height R y V

A: Given that  Radius of sphere = R       and Find volume of liquid  at height at R/2.

Q: (3)" n=0 _n!

A:

Q: Using half-angle identities, find the exact value of tan Note that (1 cos 0 1– cos 0 sin 0 tan 2 1+…

A:

Q: #3) Rewrite the integral 27 .2 p dr d0 0. in rectangular coordinates.

A:

Q: If 4x? + 5x + xy = 2 and y(2): – 12, find y'(2) by - implicit differentiation.

A:

Q: Find the area of the region that is enclosed between y = 11x? – 2³ + x and y = x? + 25x. The area is…

A:

Q: 7.2Find the macrorin series of f(x)=(1+x)^(1/3) , by reacthe term n=4

A: Follow the procedure given below.

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A:

Q: Use algebra and the properties of limits as needed to find the given limit. If the limit does not…

A: We can find the limit of the function. Firstly make factor in numerator and denominator and solve .…

Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x = x =…

A: P(x) has roots of multiplicity 2 at x=1 so (x-1)2 is a factor of P(x).  P(x) has roots of…

Q: Evaluate the given limit |. lim %3 1- x2 2. lim CosX

A: 1. limx→0+1x-1ex-12. limx→∞x1cosx

Q: 2" an 2n + 1 (-1)"-1 An 5"

A: The given sequence,1. an=2n2n+12. an=-1n-15n

Q: Given (x+ y}* – ( x - v}² = x* + y^, find dy/dx using implicit differentiation. A. - 2- E. None of…

A: Given x+y2-x-y2 =x4+y4. We have to find dydx  using implicit differentiation.

Q: L Find the point/s of intersection of each of the following figures given below, draw the element…

A: topic - Area bounded by curves

Q: Using the fundamental theorem of calculus, find the area of the regions bounded by y=8-x, x=0, x=6,…

A:

Q: 1. Which value of k will make the lines: r = (1,2) +s(2,3), s e R and 9x + ky = 0 parallel? 2.…

A:

Q: 7. Find the price per unit p that produces the maximum profit given

A:

Q: Q2 Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

A: