Curve: r(t) = b cos ti+ b sin tj + V1 - 6² tk t= 2n [c) t = 0 9. One turn of a helix

Q: Limits Evaluate the following limits using Taylor series.

A:

Q: Begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph...

A:

Q: b* – 1 Show numerically that for b = 2 and b = 4, lim x→0 appears to equal In 2 and In 4, respective...

A: Given limit:  

Q: Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the ...

A:

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the gra...

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at ...

Q: Why are trigonometric functions ideally suited to model phenomena that repeat in cycles?

A: Trigonometric functions sin, cos, tan, cosec, sec, and cot are periodic functions. That is after som...

Q: Show that there is no solution to the boundary value problem y" + 4y = 0, y(0) = 0, y(π) = 1.

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Q: The function f(x) = ∛x is one-to-one. For the function,a. Find an equation for f -1(x), the inverse ...

A: We write f(x)=y, then we switch x and y then we solve for y.    

Q: Give the formula for finding the distance between two real numbers a and b. Use the formula to find ...

A:

Q: Plz solve the b part of the question

A: It is not possible to take a dot and cross product of a scalar with a vector.

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given...

A: We have given the integral function; We know the trapezoidal rule;

Q: sin(x2 + y?)dA, where 34. Calculate D = +

A:

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫sin 3x dx, u = 3x

A: Now put

Q: Test the functions for local maxima and minimaand saddle points. Find each function’s value at these...

A:

Q: What are horizontal and vertical asymptotes? Give examples.

A: Horizontal asymptotes Any line parallel to X-axis (i.e y = a) is called a horizontal asymptote of th...

Q: Find the derivative of the function. f(x) = ((x2 + 3)5 + x)2

A: We use the power rule and chain rule.  

Q: Unit tangent vectors at a point Find the unit tangent vector at the given value of t for the followi...

A:  

Q: Approximate the area under the graph of F(x) = 0.7x° + 7x - 0.7x-7 over the interval [-7,-2] using 5...

A: Given, The area under the graph of f(x) using the left Riemann sum is given by where,

Q: Find the limits

A: We first try to find the limit by substitution. 

Q: Differentiate by using implicit differentiation x2y+xy2=6

A:

Q: find an antiderivative for each function. Do as manyas you can mentally. Check your answers by diffe...

A: Now the derivative of -cosx is sinx, therefore

Q: Limits involving transcendental functions Analyze the following limits after determining the continu...

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: #02question......and#03question

A: Since you have asked multiple questions, we will solve the first question (Question 2) for you. If y...

Q: Multiply:[(x - 7/x - 1)] . [(x2 - 1/3x - 21)].

A: We first factor the expressions  

Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each co...

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Q: Does the given graph (see attached) represent function that has an inverse function?

A: Horizontal line test: If we draw horizontal lines through the graph and if the lines cut the graph o...

Q: Solve

A:

Q: Evaluate each limit and justify your answer. lim 1x - 3x° - 1240 xS0

A: We need to find the limit  

Q: How are vectors added and subtracted geometrically? Algebraically?

A: Vector addition or subtraction can be done by Geometrically by two methods. Let there are two vector...

Q: Find the limits

A:

Q: Evaluate the integral || (x + y)e**-y dA by making an appropriate change of

A: Given data:     The given integral is: . The first equation is: x-y=0 The second equation is x-y=3. ...

Q: Find the centroid of the solid bounded above by the sphere ρ = a and below by the cone Φ= π/4.

A:

Q: Use partial fractions to find the indefinite integral ∫ (4x2 + 2x − 1) / (x3 + x2) dx

A: We need to find the integral Using Partial Fraction.

Q: Calculus Question

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Q: Use the graph of the function to identify its domain and its range.

A: Domain is the x values and range is the y values.     

Q: True or false: f(g(x)) = f(x) . g(x)_________

A: Let f(x)=2x and g(x)=x+1 Then f(g(x))=f(x+1)=2(x+1)=2x+2 f(x) . g(x)= 2x(x+1)=2x2+2x      

Q: Rationalize the denominator : 1/√7

A: Given: 1/√7 To Find: Rationalize the denominator.

Q: Calculate the following limits using the factorization formula x" - a" = 1x - a21x"-1 + ax"-2 + a?x"...

A:

Q: Find the gradient fields of the functions g(x, y, z) = xy + yz + xz

A:

Q: sketch the region described by the followingspherical coordinates in three-dimensional space. 0 ≤ρ ≤...

A: Given: The region bounded by 0 ≤ρ ≤ 1, π/2 ≤ f ≤ π, 0 ≤ θ ≤ π.

Q: Use a graphing utility to graph the function f(x) = -√(16 - x2).Use the graph to determine whether t...

A: The graph is,

Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.006t +0.8t where ...

A: The given rate of memorizing words is,

Q: Simplify or perform the indicated operation (and simplify, if possible), whichever is appropriate : ...

A:

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

A:

Q: Simplify (A-1( BA-1)-1BA-1)-1

A: Consider the equation Using the property of the Inverse of a matrix we can simplify the equation as...

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.