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Calculus
Solve the following problems. Show complete solution.
1. Find the volume of the parallel piped with the vertices in the given order: (0, 0, 0), (3, 0, 0), (0, 5, 1), (2, 0 , 5), (3, 5, 1), (5, 0, 5), (2, 5, 6), and (5, 5, 6).
Calculus
For which values of a and b is the following equation true?
lim((sin(2x)/x^3)+a+(b/x^2))=0,x approaches to 0
lim((sin(2x)/x^3)+a+(b/x^2))=0,x approaches to 0
Calculus
(a) Suppose that z = f(u) and u = g(x, y). Draw a tree diagram, and use it to construct chain
rules that express ∂z/∂x and ∂z/∂y in terms of dz/du ,
∂u/∂x, and ∂u/∂y .
(b) Let z = f(x ^2 − y^2). Use the result in part (a) to show that
y∂z/∂x + x∂z/∂y = 0
(c) Suppose yz = ln(x + z). Use implicit differentiation to find ∂z/∂x and ∂z/∂y
rules that express ∂z/∂x and ∂z/∂y in terms of dz/du ,
∂u/∂x, and ∂u/∂y .
(b) Let z = f(x ^2 − y^2). Use the result in part (a) to show that
y∂z/∂x + x∂z/∂y = 0
(c) Suppose yz = ln(x + z). Use implicit differentiation to find ∂z/∂x and ∂z/∂y
Calculus
Let p= sin t i + cost j + tk, What is |dp/dt|?
Calculus
State whether the following statements are true or false. Give reasons for your answers 3) The domain of the f/g where f(x, y) =2xy and g(x, y) =x^2+y^2 is R^2.
Calculus
State whether the following statements are true or false. Give reasons for your answers (1) The function f:R^3®R, given by f( x, y, z) =|x|+|y|+|z| is differentiable at (2, 3,-1).
Calculus
State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (4) The function f:R®R, defined by f(x) =x|x|, is an odd function. (5) The domain of the function f(g(x)), where f(x) =√x and g(x) =√2-x, is [-infinite,2.
Calculus
State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (3) The graph of every function from [0, 1] to R is infinite
Calculus
check whether the limit of the function f (x,y)=3x^3y/x^6+2y ^2 exists as (x,y) -(0,0)
Calculus
Find the two repeated limits of the function f(x,y)=(y-x/y+x)(1+x^2/1+y^2) at (0,0).Does the simultaneous limit of f exist as (x,y) -(0,0)?Give reasons for your answer
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#333702 on Dec 2022
#333702 on Dec 2022