6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos t, t), 0 < t < n. (a) v27? (b) 구 (c) v2(2+*) (d) 2 (e) 2+교 e a 112

Q: The cubic y = ax3 + bx? + cx + d tangent to the line y = 12x + 13 at (-1, 1) and have a horizontal…

A: Solution...

Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

A:

Q: ind the fangent line for... 1x1) = +²+et ( (1) = sh (k) + t at t=0 B) r(e) = sinG + case at 6: T

A: Explaination of the answer is as follows

Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

A:

Q: 6. (a) Let f(x, y) = x³y*. Find the directional derivative of f in the direction of T = (3, 4) at…

A:

Q: Show that the inflection points of the curve y=sinxxy=sin⁡x/x lie on the curve y2(x4+4)=4.

A: Given: To prove that the inflection points of the curve y=sinx/x lie on the curve y2(x4+4)=4.

Q: Q4) Show that the point (-1, 0) lies on the curve 6x² + 3xy + 2y2 + 17y – 6 = 0. Then find the…

A: Put x=-1 and y=0 in the equation of curve that is…

Q: EX: Find the F.T. of the triangular pulse: g(t) = AA ( + ) Sols Apply differentiation property of…

A: We need to derive the expression: Aτ2sinwτ4wτ42 from the expression: 8Aw2τsin2wτ4. The expression:…

Q: (z)dz

A:

Q: x* + y - 2x + 4y = 20. Write the equation of AB“ in slope-intercept form.

A:

Q: An object moves in a straight line so that its velocity after t seconds is v(t) = 2/t – t. Determine…

A: Given, Velocity of the particle v(t) = 2t -t Particle is moving in the straight line We have to find…

Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

A:

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

A:

Q: Q4) Show that the point (-1, 0) lies on the curve 6x2 + 3xy + 2y2 + 17y - 6 = 0. Then find the…

A: Substitute x=-1 and y=0 in the given equation Then 6(-1)2+3(-1)(0)+2(0)2+17(0)-6=0

Q: Find y in terms of x. dy aY = x 4(x 5 - 3) 2, curve passes through (1, 5) dx 17 (A y = (x5- 3) 3 +…

A: Consider a given differential equation isdydx=x4x5-32.The curve passes through the point 1,5.Express…

Q: 4. Let f (x) = x³ -x² + 5. a) Find the y-intercept of f. y-intercept: b) Find f' and f", and…

A: Topic: calculus As per our guidelines we are supposed to answer only three subparts of a question.…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.