Find the limit. lim (t i - 7 j+ 1? k) t→3 lim (t i – 7 j+² k) = i+ j+ k i i i

Q: Plot the point whose polar coordinates are given. (4, 9/4)

A: The objective of the question is plotting the point in the polar co-ordinates and choose the correct…

Q: TE: Round your answer to two decimal places when neec r(t) = cos(nt)i – In(t)j+ vt – 12k - omain is:…

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A:

Q: Find the limit. If you use L'Hopitals Rule, make sure to justify why you can use it. f(x) 40 g(x)…

A:

Q: Let fx) = mx + b where m and b are constants. If lim fx) = 1 and lim Ax) = -1, determine m and b.

A: Given: fx=mx+b And limx→2fx=1 and limx→3fx=-1

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t°j dt

A:

Q: 2x + 3 x 1

A:

Q: determine the interval and radius of convergence 1 Z-3)2+"(n² + 1) (4x - 12)" n=0

A:

Q: 2. A cylindrical plastic container with a radius of 15 cm is being filled with orange juice at a…

A:

Q: . Find f 6x5-25x*+8x3 +43x2-8x-12 (3x-11x3+9x2-11x+6)(9x2+12x+16) dx if this can be reduced to…

A:

Q: 4. Evaluate: lim (a² + e-*)(= cac r) エー→0+

A:

Q: Determine whether the vector field F(x, y, z) = x'5 i + y'5 j + z!5 k is free of sources and sinks.…

A:

Q: lim (- 3" n→+00

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Verify the formula F.n dS div FdV in the Divergence Theorem by evaluating the surface integral and…

A:

Q: To rationalize the denominator of 45 what value should the numerator and denominator be multiplied…

A: We can answer the question as below.

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: Does the following graph represent a function that satisfies the following condition f0) = -2, lim…

A: Topic:- calculus

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: Using any method, find the value of F. dr if F(x, y) = (8e" + 2ye") i+ (2e" + 8xe") j and C:r(t) =…

A: To find the given line integral.

Q: y8. |cosx-sinx|dx 16. J-

A: To integrate.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6…

A: Given problem:-

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A:

Q: 3. Suppose that the revenue in selling x tables is equal to 200x – 0.25x2 dollars, and producing a…

A: Suppose that the revenue in selling x tables is equal to 200x-0.25x2 dollars, and producing a table…

Q: 3x+2 dy for y = In, dx 2. Find Fully simplify your answer 3x-2

A: Solving the problem by finding the derivative.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: Using any method, find the value of F. dr if F(x, y) = (8e" + 2ye")i+ (2e" + 8xe") j and nt C:r(t) =…

A:

Q: dy 1. Find for the following: dr :b. y sin y = ry

A:

Q: Use the Integral Test to determine whether the series > 'n² +1 is convergent or divergent. n=1 Show…

A: To determine whether the given series is convergent or divergent.

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim tto0 2t2 +3' 2t (?,?)

A:

Q: For the linear transformation T: R* - R, T(v) = Av, find T(1, 0, 2, 3) and the preimage of (0, 0,…

A:

Q: Solve the initial value problems: y^ prime =6+5y+y^ 2 ; y(0) = 0

A: We need to solve D.E.

Q: dy 1. Find for the following: - dr f. 4x² - 9y² = 36 g. -+-=1 X y ... h. 3x°y+2xy² = 4 i. (3 - 2x) =…

A: f.4x2-9y2=36Differentiate w.r.t.x4×2x-9×2ydydx=08x-18ydydx=08x=18ydydxDivide18y on both…

Q: find the tangent plane to the surface z = y-x at the point (1,2,1)

A:

Q: Determine the area to the left of g(y) = 3-y2 and to the right of x = -1

A: Area

Q: dy dr a. r+y = 8 Find for the following=

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: 21 · 8* cos (8*) dx =

A:

Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

Q: Differentiability of f(r, y) at point (a, b) Let f: R R be a function given by if (r. y) (0.0). f(r,…

A: Given

Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on…

A: Question is solved step by step.

Q: Evaluate CF dralong the line segment C from P to Q. F= x j; P(3,2), Q(3,8) SCF dr- i

A:

Q: Compute the Laplace transform of 10 + 5t + t2 – 4t3

A:

Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

A:

Q: 1. Find parametric equation for the line through the point P(3,-4,-1) parallel to the vector v…

A:

Q: Chain rule and implicit differentiation Suppose that F(r, y, 2) = 0 defines z as a function of z and…

A:

Q: This is a graph of f'(x), the derivative of f(x). At which of the marked values is: f(x) greatest?…

A:

Q: 'ind the work done by the three-dimensional inverse-square field (r) = r on a particle that moves…

A: Given problem:-

Q: An isotope of the element erbium has a half-life of approximately 9 hours. Initially there are 7…

A:

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: Here, the given concentration function is: C(x)=0.9x2 where x is the distance away from the plant in…