where r is the position vector 6. Show that A) - da = | (Ax (Vf)) · da + fA- dl 7. Evaluate the following integrals: (a) 8(r – 1)dr (b) (2² +3)6(x – 5)dr (c) rő(r*. | z6(r – 5)dr -5 (d) 9r*6(3x + 1)dr

Q: Use synthetic division to show that I= 6 is a root of the equation z - 12z - 4r + 240 = 0. Use the r...

A:

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: (b) Find öw/ds and öw/dt by converting w to a function of s and t before differentiating. aw %3D ds

A: w=xyzx=s+2ty=s-2tz=st2To find ∂w∂s and ∂w∂t

Q: If gw + xcos tgcx) = x7, find gro) g'co) =

A: We have to find

Q: 6) At 4:00PM, a thermometer reading of 28°C is taken outside where the ambient temperature is -11°C....

A: Answer is mentioned below

Q: Suppose that in 1653​, a man bought a diamond for ​$26. Suppose that the man had instead put the ​$2...

A:

Q: (a) For what value of x does f(x) = g(x)? X= (b) For which values of x is f(x) > g(x)? For every x i...

A: We can solve the problem by the criteria of interse

Q: (a) Is the vector field F(x, y) = (xe", ye") conservative? Justify your answer. If it is conservativ...

A: Let's find. 

Q: Consider the solid that lies above the square (in the xy-plane)R=[0,2]×[0,2], and below the elliptic...

A: Here is the solution of the given problem.

Q: Instructions: Please enter the integrand in the first answer box. Depending on the order of integrat...

A:

Q: Let f(x) = -2 and let g be the function defined by (x – 3)(r – 5) if r 3 (a) Evaluate lim(f o g)(x)...

A:

Q: Find the exact arc length of the curve y =2V on the interval [0,11]. 70 +60 +50 +40 +30 +20

A: The objective of the question is determine the arc length of the given curve.

Q: Integrate: 4t² + 7t – 9 dt

A:

Q: Given (x² – y²)² = 4ay², find y".

A: Let's find. 

Q: Vhich of the following is correct about the statement: "A separable DE is also an exact lifferential...

A: We have to find

Q: 1 12.) dx x2 V25 – x2

A: We have to find

Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y...

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: An office supply company sells x permanent markers per year at p dollars per marker. The price-deman...

A: a) Demand : p=100-0.001x Cost : C(x)=5000+2x Revenue=Price * Quantity So, R = px To maximize revenue...

Q: Use a graph below of f(x) = 3e¬5z° to estimate the x-values of any critical points and inflection po...

A: Given: f(x)=3e-5x2 Critical points are points where the function is defined and its derivative is ze...

Q: Explain the expressions. Please detailed explanation!!! AA = @ 33 (elepticity) aA (anisotropy factor...

A: These are some of the grounding formulae of photophisics.  θ is the ellipticity  ΔΑ  is the circular...

Q: 4. Here is some data about Ivan Khatchatourian, one of the instructors for this course, at two diffe...

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min....

A: Take the volume formula and derivative it with respect to t

Q: find the area of the shaded sector pictured below. Round to the nearest tenth. r=4.8 θ=50

A: Given,           The circle is shown below with r=4.8 and θ=50°              

Q: Calculate the difference quotient for f(x) = x + x at a = 11. (Express numbers in exact form. Use sy...

A: Topic = Application of derivative

Q: 3. Let f be the function defined by f(x) = x° + 2x + g(x) = f¯²(x), find gʻ(12). A. 1 В. 1/11 С. 1/9

A:

Q: y= f'(x) 2 8 x (a) On what interval(s) is f increasing? (Enter your answer using interval notation.)...

A: Find interval of function increasing, local maximum and local minimum, interval of concavity, point ...

Q: Graph the function f(x)=−x^2−10x by starting with the graph of y=x^2 and using transformations​ (sh...

A: Consider the function  f(x)=−x2−10x

Q: determine whether the series is convergent or divergent. the sum of n=1 to infinity of (1/2^n+6/n)

A:

Q: Consider the function 1 f(x) = x² el/x 2 (a) Find the vertical asymptotes. Answer: x = (b) Find the ...

A:

Q: Suppose that 3x - 5 f(æ) x + 6 (A) Find all critical values of f. If there are no critical values, e...

A: Follow next step

Q: Answer the following questions for the function f(x) = xV a? + 4 defined on the interval -6, 7|. a.)...

A:

Q: A. By simple integration rules 1. fki+3x-2 + 5x+)dx 2. s**-5x²+4x dx (x-1) 3. S*- x3 -343 dx X-7 4. ...

A:

Q: Determine the volume of the solid lying under the graph of z = x + 3y

A:

Q: If f(3) = 7 and f ′(x) ≥ 2 for 3 ≤ x ≤ 5, how small can f(5) possibly be? f(5) ≥

A:

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 – 32x² + 9 (a) Find...

A: Here we have to find the interval on which f is concave up.

Q: Find f, fy, and f,, and evaluate each at the given point. z' fix, y, 2) %3D х*уз + 2хyz - 8yz, (-3, ...

A: We will do partial differentiation.

Q: 4. Find the equation of the tangent line to f = 10** at x = 0. А. у %3D 1 B. x = 1 D. y = x – 1 E. y...

A: Tangent line equation =>y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate ...

Q: A certain office can purchase a photocopier for $5400 with a maintenance fee of $15 a month. On the ...

A:

Q: Find the first three non-zero terms in the taylor series of f(x) = (x + 5)* about x = a where a = 2.

A:

Q: dy CSC X Find for y 3= dx 1+cSC X dy dx

A: We have to solve

Q: PLS HAVE A NEAT PENMANSHIP

A: We have to solve

Q: 77 x 35 =

A:

Q: Find the area of the shaded sector. Round to the nearest tenth. r=6 θ=94

A: The shaded sector has radius r=6 and θ=94°

Q: Es) A child is retrieving a wheeled toy that is attached to a string by pulling in the string rate o...

A: Let the distance between boy and toy is ' x ' at a particular instant.

Q: Consider the effect of gravity on falling objects. If you drop an object, from rest, on earth, it wi...

A:

Q: A mathematician stands on a beach with his dog at point A. He throws a tennis ball so that it hits t...

A:

Q: Use the initial condition to find the particular solution of the differential equation. Differential...

A: topic - differential equations

Q: Based on your knowledge of the behavior of the numerator and denominator, predict the value of sin a...

A:

Q: HR MIN SEC n6 of 6 Calculate the first, second, and third derivatives of 12 y(x) = 42+x (Use symboli...

A:

Q: Use l'Hospital's Rule to evaluate the limit. cos(x) lim z-* 1- sin(x) Limit:|

A: To find:limx→π2+cosx1-sinx