This is a hard question whaich found in UKMT question test online

This is a hard question whaich found in UKMT question test online

Evaluate the following integral using any Vector Calculus method The integral with bounds C; [(4+eyz)i+(xzeyz+2yz)j+(6z2+xyeyz+y2)k] dot dr, where C is the part of...

The integral with bounds C (xyzi+y4j+(2y+z8)k) dot dr, where C is the intersection of the unit cube and the plane z=x/10+y/20+1/30; Specific which method you used.

The vector from the point (1,2, -3) to the centre of the sphere x2+y2+z2-kx+3y-lz=1 is given by < 3, h, -2 > . Then the value of hkl is?

I need some help using vectors to find the area of this parallelogram. I use three points to create two vectors with the same initial points and use a 2x2 determinant to compute the cross...

Consider the solid body which lies above the upper half of the cone x^2 +y^2= 3z^2 and below the sphere x^2 + y^2 + z^2 = 4z. Assume this body is of constant density. Use...

Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the...

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis...

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In this lesson plan I explain the idea of delta-epsilon proofs and develop some notions of limits in the setting of several variables....

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This is a more thorough study of the general n by n determinant. I use it as optional lecture in my Multivariate Calculus course.

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This is a 3rd lecture on Multivariate Calculus, where I give an intuitive development of the determinant.

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This is my second lecture on Multivariate Calculus, where I motivate and explain the dot product.

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This lesson plan introduces vectors and vector operations. It is my first lesson on Multivariate Calculus.

triple integrals

∫∫ √(4v2 + 4u2 + 1) dvdu, with limits of integration 0≤v≤1 & 0≤u≤2 *Note: the entire expression is supposed to be under the square root symbol I have tried...

Containment and Equality If A and B are sets, then A is said to be contained in B iff (if and only if) every element of A is contained in B. So A⊆B means that A is a subset of B. Example: All squares ⊆ all rectangles All right triangles ⊆ all triangles Important! This implies the idea of forwards and backwards logic: If Joe has three million dollars, he is a millionaire... read more

Sets and Other Elementary Subjects Sets are a collection of things called objects. Objects are all unambiguously defined. In other words, objects have unmistakably clear definitions with one meaning and one interpretation that leads to one conclusion. This may seem convoluted because we are so used to words and phrases having different meanings and whatnot, but not in this case. Look... read more

0∫2(0∫¶/2 xsin(y)dy)dx

A person's BMI is given by I(W,H) = W/H^2, where W is the person's weight in kilograms and H is height in meters. Suppose I am 1.65 meters tall and weigh 54.5 kilograms. After a month, I become 1...

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