x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

Q: Use the definitions of the hyperbolic functions to find eachof the following limits. limit x appraoa...

A: Consider the follow formula: tanhx=ex-exex+ex

Q: What is a trace of a surface?

A:

Q: ii) How would you describe geometrically the relationship between a nonzero complex number z = a + i...

A: Given: Describe geometrically the relationship between z=a+ib anda. −zb. z−1  

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫sec 2t tan 2t dt, u = 2t

A:

Q: Find the vector in the direction of (5, – 12) with length 3.

A: To find: A vector in the direction of 5,-12 with length 3.

Q: Find the product : (2 - y5)(2 + y5).

A:

Q: Area A rectangle is inscribed in a semicircle of radius 10, as shown in the figure. Find a function ...

A: Given Data The radius of the semicircle is R=10. The width of the rectangle is h.   Consider the len...

Q: Sketch the regions defined by the polar coordinate inequalities 0 ≤ r ≤ 6 cos θ

A: Try to graph the following equality:

Q: Determine the order and degree based on the given differential equation.

A: Order of a differential equation is given by the highest derivative present in the differential equa...

Q: Designing exponential growth functions Complete the following steps for the given situation.a. Find ...

A: In year 2016, the population is 90000. Population grows at a rate of 2.4%/year.   To find: 1. k 2. t...

Q: Calculus Question

A: The given trigonometric ratio is : sin-π12 Since, -π12=π4-π3. So replace -π12 with π4-π3 in sin-π12....

Q: The table below shows total expenditures for colleges and universities in millions of dollars. All d...

A: Interpolation Method: It is used to determine the missing values of the table by estimating from th...

Q: Let f(x) = x3 – 8x². Find the points on the graph of f where the tangent line is horizontal. (Enter ...

A:

Q: Find the general solution of the differential equation y′ey−3x = ex+2y

A: Consider the given equation is written as, dydxey-3x=ex+2yey-3xdy=ex+2ydxeye-3xdy=exe2ydxe-ydy=e4xdx...

Q: 2 The consumption function of a certain country is given by 1000VI+ 701 - 0.8 C = where I is the nat...

A:

Q: Use properties of logarithms to condense the logarithmic expression, 4 ln(x +6) - 3 ln x. Write the ...

A:

Q: 4y" - 4y' + y = 0

A: Given differential equation is: 4y" - 4y' + y = 0 Consider the corresponding characteristic equation...

Q: What are limx→+-∞ k (k a constant) and limx→+-∞ (1/x)? How doyou extend these results to other funct...

A: limx→af(x)=L means f(x) becomes arbitrarily close to L as long as x is sufficiently close to a.  We ...

Q: The following table shows the percentage of a country's college freshmen in the given year who belie...

A: Given, Year 1996    2000    2004 2008 2012 Percentage 56.3 53.6 53.6 58.5 61.1    

Q: Determine whether the statement" The weight of a car is a scalar", is true or false. If it is false,...

A: Scalar: Many quantities in geometry and physics, such as volume, mass, temperature and time can be c...

Q: Find the arc length of the curve on the given interval. (Round your answer to two decimal places.) ...

A:

Q: Find two power series solutions of the differential equation (x² + k)y" + 3xy' – y = 0 at x = 0. whe...

A: Given (x2+k)y''+3xy'-y=0 at x=0 where k=9 Let us consider  y=∑kckzk Differentiate y we get y'=∑kkckz...

Q: continuous femelion function for all ralies ef f escept thane ralues for inhich the denorinator is s...

A: Consider the given statement, A ---- function is a continuous function for all real values of x exce...

Q: Write the first six terms of the arithmetic sequence: an = an-1 -10, a1 =30

A: The given sequence is an=an-1-10 And first term is a1=30. Since, first term is given, so we have to ...

Q: 16a

A:

Q: a7,8

A: Consider the general equation of a plane, 4x-2y+7z+12=0 the normal vector of this plane will be give...

Q: Use the properties of the derivative to find the following.                                (a) r′(t)...

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want an...

Q: Change of variables in a Bernoulli equation The equationy '(t) + ay = byp, where a, b, and p are rea...

A: Consider the first differential equation: y't+y=2y2                   ...... 1 Compare equation 1 wi...

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c...

A:

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2...

A: Given rectangular equation can be written as x2-y2-2z2=0. The co-ordinates in terms of spherical co-...

Q: 7 3 -4 1 -1 0 0 0 1 -2 1 3 7. 1

A: Since, you post multiple question. I am answering first one.Please post again for remaining parts wi...

Q: Differentiate the function y=ex(sinx−cosx).

A: y=exsinx-excosx.  

Q: How would you approximate e-0.6 using the Taylor series for ex?

A:

Q: Substituting this back into the function, we have lim (6 + h)3 - 216 lim (216 + 108h + 18h2 + h') – ...

A: Expand 6+h3 as follows. 6+h3=63+362h+36h2+h3                  a+b3=a3+3a2b+3ab2+b3=216+108h+18h2+h3 ...

Q: i) Find real and imaginary part of complex number (V3 + i)° by using De Moivre's Theorem.

A: Consider the complex number: 3+i3 Comparing the complex number 3+i with standard form of complex num...

Q: Consider the following function. f(x) = −x2 − 18x − 4 Find its average rate of change over the int...

A:

Q: a2

A: Given:          a→=i→+j→-2k→b→=3i→-2j→+k→c→=j→-5k→

Q: Consider the following matrix 3 1 -2 A -1 1 1 1 0 a) By evaluating the determinant of A determine in...

A:

Q: 5. Suppose that the function f has continuous first and second derivatives. The following table prov...

A: Given,

Q: Differentiate the inverse trig function  y=Sin-1(Cos x/1+Sin x)

A: We use the chain rule and the quotient rule to find the derivative. y=sin-1cosx1+sinxy'=11-cosx1+sin...

Q: Among all pairs of numbers whose difference is 16, find a pair whose product is as small as possible...

A:

Q: 1 Piecewise Defined Functions Evaluate the piecewise defined function at the indicated values. S5 2x...

A: the given function is  f(x)=5,                  if x≤22x-3,          if x>2

Q: decide if the given statement is true or false,and give a brief justification for your answer.If true...

A: The values of x,y for which the functions in an autonomous system vanishes are equilibrium points.  

Q: Using Logarithmic differentiation, find F(x) F(x)=x8/ex(x-1)

A:

Q: a4

A:

Q: Factor completely. 10x2(x + 1) - 7x(x + 1) - 6(x + 1)

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.