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What is the value of $\;$ $\lim_{x\to 0} \large \frac{log(1+x)}{x} $?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

What is the value of $\;$ $\lim_{x\to 0} \large \frac{a^x-1}{x}$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

What is the value of $\;$ $\lim_{x\to 0} \large \frac{e^x-1}{x}$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

What is the value of $\lim_{x\to 0} \large \frac{sin^{-1}x}{x}$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

What is the value of $\lim_{x\to 0} \large \frac{tan^{-1}x}{x}$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

What is the value of $\;\lim_{x\to 0} \large \frac{tanx}{x}$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

What is the value of:$ \;\lim_{x\to a} \large \frac{x^n-a^n}{x-a}$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

Which of the following is not a property of coninuity? $\qquad$(A) Every Constant Function is Continous, $\\$ (B) Every Polinomial Function is Continous, $\\$(C) Every Differential Function is Continous, $\\$(D) Every Continous Function is Differntiable.

asked Apr 4, 2013 by balaji.thirumalai

1 answer

True or False: Every Constant Function is Continous

asked Apr 4, 2013 by balaji.thirumalai

1 answer

True or False; Every Continous Function is Differntiable.

asked Apr 4, 2013 by balaji.thirumalai

1 answer

Let f be a real function on a subset of the real numbers and let c be a point in the domain of f. For f to be continuous at c $\; \lim_{x\to c} f(x)$ should equal what?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

True or False: A Function is Continous if it is continous on the whole of its domain.

asked Apr 4, 2013 by balaji.thirumalai

1 answer

True or False: If a function $f: X \rightarrow Y$ is invertible, it has a unique inverse.

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) True or False: \[ (f . g) oh = (foh) . (goh)\]

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\). True of False: \[ (f + g) oh = (foh) + (goh)\]

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Given a square matrix $A$, let $adj (A)$ be the adjoint, and $C$ be the cofactor matrix of $A$. Which of the following is a representation of the adjoint of A, i.e, $adj (A) = ?$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If the Minor of an element $a_{ij}$ is denoted by $M_{ij}$ and the cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ then, which of the following is true?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If the Minor of an element $a_{ij}$ is denoted by $M_{ij}$ and the cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ then, which of the following is true?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the area of a triangle with vertices (x1, y1), (x2, y2) and (x3, y3)?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

True or False: If to each element of a row (or a column) of a determinant the equimultiples of corresponding elements of other rows (columns) are added, then value of determinant remains same.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

True or False: The determinant of the product of matrices is equal to product of the individual determinants, $det(AB) = det(A).det(B)$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If we multiply one row a matrix by k, i.e, $\begin{vmatrix} ka& kb\\ c& d\end{vmatrix}$, then which of the following is also the value of the determinant?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If any two rows or any two columns in a determinant are identical (or proportional), then which of the following is true?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

In a square matrix, If we interchange any two rows (or columns),which of the following is true?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

True or False: Any square matrix A and its transpose have the same determinant.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of the determinant of the following 3x3 matrix: $\begin{vmatrix} a&b&c \\ d&e&f \\ g&h&i \end{vmatrix}?$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the determinant of 2x2 matrix $\begin{vmatrix} a & b\\c & d\end{vmatrix}?$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: For every ______ matrix A of order n, we can associate a number called determinant of the matrix A, written as det A, where aij is the (i, j)th element of A.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Which of the following is equal to $cos\;3x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $3\:sinA-4\;sin^3A$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $2\;tan^{-1}x$ given $–1\leq x \leq 1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $2\;tan^{-1}x$ given $x \geq 0$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $2tan^{-1}x$ given $–1 < x < 1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1}x- tan^{-1}y$ given $x<0$, $y>0$ and $xy<-1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1}x- tan^{-1}y$ given $x>0$. $y<0$ and $xy<-1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1}x - tan^{-1}y$ given $xy > -1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1}x+tan^{-1}y$ given $x,y >0$ and $xy >1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1}x+tan^{-1}y$ given $xy <1$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cos^{-1}x-cos^{-1}y$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}(x) - sin^{-1}(y)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cos^{-1}x+cos^{-1}y$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}(x) + sin^{-1}(y)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cosec^{-1}(x)+sec^{-1}(x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cot^{-1}(x) + tan^{-1}(x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}(x) + cos^{-1}(x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cosec^{-1}(-x)$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sec^{-1}(-x)$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cot^{-1}(-x)$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1}(-x)$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cos^{-1}(-x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

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