# Questions & Answers

### Determine a region whose area is equal to the given limit. Do not evaluate the limit.

The purpose of this article is to find the region having an area under the curve that is represented by a given limit. The basic concept behind this

### Find the points on the surface y^2 = 9 + xz that are closest to the origin.

This question aims to learn the basic methodology for optimizing a mathematical function (maximizing or minimizing). Critical points are the points

### If f and g are both even functions, is f + g even? If f and g are both odd functions, is f+g odd? What if f is even and g is odd? Justify your answers.

The main objective of this question is to check whether the addition of the given two functions when both the functions are odd, even or one is odd

### Find the values of x such that the angle between the vectors (2, 1, -1) and (1, x, 0) is 40.

The question aims to find the value of an unknown variable given in 3D vector coordinates and the angle between those vectors. The question depends

### If f(2)=10 and f'(x)=x^2f(x) for all x, find f”(2).

The aim of this question is to learn how to evaluate the values of a higher order derivative without explicitly declaring the function itself.   To

### For a test of Ho: p=0.5,the z test statistic equals -1.74. Find the p-value for Ha: p<0.5.

The question aims to find out the p-value using the given alternative hypothesis, which is a one-sided hypothesis. Therefore, the p-value will be

### Express the plane z=x in cylindrical and spherical coordinates.

This question aims to find the cylindrical and spherical coordinates of the plane z = x. This question is based on the concept of coordinate systems

### Find the probability P (E or F), if E and F are mutually exclusive.

P(E) = 0.38 P(F) = 0.57 The of this question is to find the probability of two mutually exclusive events E and F when either of them can occur. The

### Find the exponential function f(x) = a^x whose graph is given.

This problem aims to find the exponential function of a given curve, and there lies a point on that curve at which the solution will proceed. To

### (a) Find the average value f on the given interval. (b) Find c such that f_{ave} = f(c). Equation given below

This problem aims to find the average value of a function on a given interval and also find the slope of that function. This problem requires

### Find a single vector x whose image under t is b

Transformation is defined as T(x)=Ax, find whether x is unique or not. This question aims to find the uniqueness of vector $x$ with the help of

### Let P(x,y) be the terminal point on the unit circle determined by t. Then find the value for sin(t), cos(t) and tan(t).

The aim of this question is to find sin t, cos t, and tan t for a given point P=(x,y) on the unit circle which is determined by t. For this, we