Find the general antiderivative, F(x), for the given functions. a) f(x)=-sin? xcosx b) f(x) =/7-2x

Q: Consider the following equations. y = -x2 + 2x + 1 y = -x + 1

A: Solution: y = -x2 +2x +1 y =-x+1

Q: 2. Let f(x) = VI(2 – x)². Use the local linear approximation of f(x) at ro = 1 to estimate V0.99…

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: Solve the following differential equations of dy 1 y= xy': + dx

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Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Sx³cos3x?dx

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Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i+ 11 sin(t)j + tk; t= 2 T() - T N 2.

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Q: For the function shown below, determine the following: a. limf(x) b. limf(x) ズーラ2 c. lim f(x) d.…

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Q: he CEO of SWNN Chemical determ achine Usen the func

A: answer is in next step

Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = e"i+etj K(t)

A: We have to find k(t)=?

Q: dy y- 2x. dx = x(x+1)y %3D

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Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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Q: 31 + 98.6, where Tis the temperature, in degrees Fahrenheit, at time t, in hours. R+1 The…

A: The temperature T of a person during illness is given by Tt = 3tt2+1+98.6°F…

Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: The height of a right circular cone is always three times the radius. Find the volume of the cone at…

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Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

Q: Use left-to-right elimination to solve the system of equations. 3x + 4y - 5z = 8 4x + y- z = -1 x-3y…

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Q: Evaluate the integral (8x +12y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A: Topic:- integration

Q: uilding that is 225 feet tall casts a shadow of various lengths as the day goes by. An angle of…

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Q: The graph of f(x) is shown (see figure). f(x) %3D Vx2 +7 Net draw o scale (a) Find the following…

A: Solution: f(x)=9xx2+7

Q: Consider the following planes. -6x + y + z = 6 18x - 3y + 6z = 36 (a) Find the angle between the two…

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Q: derivatives as functions of

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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Q: Determine the limit of the sequence or state that the sequence diverges. n an = Vn3 + 2 (Use…

A: Given: an=nn3+2 To find:  limn→∞ an limn→∞an=limn→∞nn3+2 Given limit is of ∞∞ form

Q: r(t) = cos(Tt)i – In(t)j+ vt – 16k; to = 17 %3D Choose one▼

A: Given

Q: A plane P, in R'is perpendicular to the vector n = (6, 2, 8), and contains the point (– 9, – 1, –…

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Q: It can be shown that the polar curve r = a sin(0) +b cos(0), where ab + 0, is a circle. Find the…

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Q: A company that produces cell phones has a cost function of C = 6x² – 197x + 1859, where C is the…

A: C= 6x2-197x+1859differentiating w.r.t xC'=12x-197+0C'=012x-197=0x=19712

Q: Area of the polar graph

A: Topic:- geometry

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) logg (x) lim In(x) X00

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Q: Use linear approximation, i.e. the tangent line, to approximate V1.3 as follows: Let f(r) = VT. The…

A: f(x)=x3f(x)=x13differentiating w.r.t xf'(x)=13x-23value of m at x=1f'(1)=131-23=13f'(1)=13m=13at…

Q: Use the log rule of differentiation and differentiate y with respect to x.  y = ln( 8 + ex 8 − ex

A: given function

Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

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Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm/min. Find the rate at…

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Q: Calculate the derivative. y = 2 cosh (x) coth (x) (Give an exact answer. Use symbolic notation and…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: First we will draw graph for function.

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(4, 5, 4),…

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Q: Find the average value of y = sin x between x = 0 to x = π.

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Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: Use the principle of mathematical induction to show that the given statement is true for all natural…

A: Question number 6 has been solved as per the requirement of the student.   This question can be…

Q: Determine the range of f(x,y)=tan 2+x +y

A: Here the value of x2+x2+y3 can vary from -∞ to ∞. The possible values of tan-1x2+x2+y3 is…

Q: Find the area enclosed by the given curves. Find the area between the curves y = In x and y = In 3x…

A: Solution:

Q: uppose the area of the region betwe =b is 3 square units. Find the area be

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Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: If f(x) = V4x + 1 find f"(2). O 4/27 O 213 None of these O 2/3

A: Topic:- Derivatives

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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Q: x+2 Solve: x-1-3 <0

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Q: dy Then find the slope of the curve at the given point dx Differentiate implicitly to find…

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