1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of t at which the parametric curve x = 2 sint, y = 4 cost from t = 0 to t = 2n has (a) a horizontal tangent line and (b) a vertical tangent line.

Q: 5² - 13 ニ

A:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Find the unit tangent vector to the curve at the specified value of the parameten r(t) = 4 cos(t)i +…

A:

Q: Question 7 Use double integration to find the volume of the solid. 3 3x + 2y + 4z = 12 A) 6 B) 9 c)…

A:

Q: +1++4+ +7++10 written in sigma notation is equal to The sum 3k-5 A k=1 3k - 4 B k=1 3k-2 k=1 3k-1…

A: Let's find.

Q: Find the area of the surface that is generated by revolving the portion of the curve y= x² between x…

A:

Q: n/2 sine Evaluate the iterated integrals r cos e dr de 0.

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Find the surface area of that portion of the surface Z = 4 -x that lies above the rectangle R in the…

A:

Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

A:

Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

A:

Q: sin° xcos xdx x cos'

A: We will use substitution method to solve this definite integral.

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find V x (V × F) if F(x, y, z) = 6xyj+7xyzk. V × (V × F)

A:

Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given points,  P(0,0,0), Q(4,2,4)

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: Find the area of the region enclosed by x2 and y = 5x by integrating with respect to y. the curves Y…

A:

Q: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

A:

Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

A:

Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10 + 10 sin…

A:

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A:

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x and…

A:

Q: Use a double integral to find the volume under the plane z=38x+y and over the rectangle…

A: We have to find the volume using double integration.

Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.

Q: Find the curvature and the radius of curvature at the stated point. r(t) 2 cos(t)i+ 3 sin(t)j+ 10tk;…

A: Solving

Q: 55-58 Use the properties of integrals to verify the inequality without evaluating the integrals. 55.…

A: Let's find.

Q: 3. -2 -1 5. Find the velocity, acceleration, and speed of a particle traveling along the curve…

A:

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ï, §) = (?, ?) y = r

A:

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A:

Q: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

A:

Q: Let f(x) = 9x* + nx² + e2x. Compute f((x). (Use symbolic notation and fractions where needed.) p)…

A:

Q: Find the area of the region(s) enclosed by the curv

A:

Q: X+2 At what points is the function y = continuous? 2 X- 9x + 14 ... Describe the set of x-values…

A:

Q: Consider a field with V = 8a²y² î + 4y²j + –5y² z³k a) Find the divergence of V: V•V: b) Find the…

A:

Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

A:

Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.

Q: Find dy/de y=(1 +Sin 94)6

A:

Q: Sketch the region enclosed by the curves and find its area. y = cos 4.x, y = 0, x 8' 4 NOTE: Enter…

A:

Q: ne area Of Lhe region

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

A:

Q: 1-sine Evaluate the iterated integrals J. J. r2 cose dr de A) 1 B 2 c) o D) 3

A:

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function is: f(x)=e-5x

Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: We have to find the volume by shell method.

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A:

Q: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

A: