a) Eliminate the parameter to find a (simplified) Cartesian equation for this curve. (b) Sketch the parametric curve. On your graph, indicate the initial point and terminal point,  and  include an arrow to indicate the direction in which the parameter t is increasing.

Q: Find the minimum and maximum values of the function y = 8Vx? +1 – 5x on the interval [0, 3] by…

A: To find the minimum and maximum values of the function y=8x2+1-5x on the interval 0, 3 by comparing…

Q: dz and at dz 3. Let z x2 + y3, r 2st and y = s- t2. Compute for

A:

Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

A:

Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i…

A: The Solution is given below

Q: Evaluate the limit In(x) lim x+1 x- 15x+ 14

A: Given,  limx→1ln(x)x2-15x+14

Q: Find the sum of the convergent series. 1.6

A: Gp

Q: Q3. (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x2.

A: We have to find binomial expansion.

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: A rectangular open box is to be made to hold a volume of 50 in3. The base of the box needs to have a…

A:

Q: dA

A:

Q: X-1 4 = = 2 – y = z 2 y-2 z-1 12 = x = -1, 3 2 Show that these are skew lines.

A: To show that the given lines are skew lines.

Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

Q: 1. dr COS 2. sin

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 (Use decimal…

A:

Q: If the tangent line to y f(x) at the point (1,2), passes through the point (-1,1), then f'(1) = %3D…

A: Find f'(1)

Q: A. For each of the following functions z, find and дх 2. z = tan 出一郎

A: Explanation of the answer is as follows

Q: Topic on Application of Integration - Area. Find the point/s of intersection of the graph and draw…

A: Here point of intersection of the line y=0 and y=x2-4 is put y=0 x2-4=0x2=4taking square root on…

Q: Find the set of all values of x at which the line 3x-y+k= 0 is a tangent line to the -3 curve f (x)=…

A: We need to choose correct option.

Q: 10 Find the derivative f' (0) of f(x) = at х+4 O using the laws of differentiation.

A: f(x)=10x+4DIfferentiate w.r.t.xf'(x)=ddx(10x+4)Take constant outf'(x)=10ddx(1x+4)f'(x)=10ddx(x+4)-1…

Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

A:

Q: Test the given geometric series for convergence or divergence. If it converges, find its sum. 4 16…

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Q: To find two real numbers whose difference is 24 and whose product is minimum, we can find the…

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Q: 3s + 2 4s2 + 12s + 9 4 te 궐 | O Option 1 O Option 2 4 tet e - e 2. O Option 3 O Option 4 3/14

A: Inverse laplace

Q: "Definite Integrals" 1. sin | COS dr -

A:

Q: Question 1 Determine the inverrse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

A: L-11s-a =eat L-1as2+a2=sin(at) and L-1ss2+a2= cos(at).

Q: 5 sin(0) – cos(0) dO Evaluate: со

A:

Q: III. GRAPH ANALYSIS: The graph of f is shown below. Use it to answer A, B, and C. -7 -$ -4 -3 -2 1 2…

A:

Q: 1 0 0 0 0 1 2 -6 2 -8 10 1 0 1 0 3 -2 -5 -16 |

A: We have to multiply: 1000012-60010003-22-8-5-16

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

Q: 4. Which of the following is the Maclaurin series fore Circle all that apply. (a) (b) (-1) (2n)! (d)…

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Q: Solve for the general solution using homogeneous

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Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: x = -2t 1 - y = z – 8 and l2 2 3 Given: line l1 : 4 y = 2+ 2t z = 6+ 2t 2. Find the equation of a…

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Q: dx 8. Evaluate the integral / zlnrV(In x)² – 8 x In a V(In a)2 – 8 |

A:

Q: Find the set of all values of x at which the line 3x-y+ k = 0 is a tangent line to the curve f(x)…

A:

Q: y =, x = 1, x = 4, and y = 0 is revolved about the y – axis.

A: Let's find.

Q: derivatives power series

A:

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A:

Q: The integral sin(x- 2) dx is transformed into f, g(t)dt by applying an appropriate change of…

A:

Q: 1- x² tx

A:

Q: Convert to degrees and write it as the least possible positive coterminal angle. a. -220° b. 120° C.…

A: We have to find the angle

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

A:

Q: 4. Let z = x2+y, x 2st, y = s - t2, s = u", and t = usin w. Compute for

A: To find the partial derivatives using chain rule

Q: Problem #4: Find the slope of the line tangent to (х-3) + (y-2)² = 1 at (3,7). the conic section 36…

A:

Q: 10. A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so…

A: A conical paper cup is 10 cm tall with a radius 10 cm. The cup is being filled with water so that…

Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

A:

Q: Find the volume oF the solid obtained by rotating about the x- axis oF the region bounded by y= *,…

A: A detailed solution is given below.

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: The circumference of a sphere was determined as 84 cm with a possible error of 0.5 cm. Estimate the…

A: We will use the formulae of circumference and volume of sphere to solve this question.

Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx