according to ques,
Differentiate x/sinx w.r.t sin x.
according to ques,
If x = asin2t (1 + cos2t) and y = b cos2t (1–cos2t), show that
\[x~=~asin2t~(1\text{ }+\text{ }cos2t)~and~y~=~b~cos2t~(1cos2t)\]
Find dy/dx of each of the functions expressed in parametric: If x = ecos2t and y = esin2t, prove that dy/ dx = – y log x/ x log y.
\[x~=~{{e}^{cos2t}}~and~y~=~{{e}^{sin2t}}\] So, \[cos\text{ }2t\text{ }=\text{ }log\text{ }x\] and \[sin\text{ }2t\text{ }=\text{ }log\text{ }y\]
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Find dy/dx of each of the functions expressed in parametric: x = 3cosq – 2cos3q, y = 3sinq – 2sin3q.
\[x\text{ }=~3cosq\text{ }\text{ }2co{{s}^{3}}q,~y~=\text{ }3sinq\text{ }\text{ }2si{{n}^{3}}q.\]
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Differentiate :
according to ques,
Differentiate :
according to ques,
Differentiate :
according to ques,
Differentiate :
according to ques,
Differentiate :
according to ques,
Differentiate :
according to ques,
Differentiate :
according to ques,
DIFFERENCIATE: sinm x . cosn x
ACCORDING TO QUES,
DIFFERENCIATE: (sin x)cos x
ACCORDING TO QUES,
DIFFERENCIATE:
ACCORDING TO QUES,
DIFFERENCIATE: sin x2 + sin2 x + sin2 (x2)
ACCORDING TO QUES,
DIFFERENCIATE:
ACCORDING TO QUES,
Differentiate: sin (ax2 + bx + c)
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
A function f : R ® R satisfies the equation f ( x + y) = f (x) f (y) for all x, y ÎR, f (x) ¹ 0. Suppose that the function is differentiable at x = 0 and f ¢ (0) = 2. Prove that f ¢(x) = 2 f (x).
\[f\left( x \right)\text{ }=\text{ }2f\left( x \right).\]
Show that f (x) = |x – 5| is continuous but not differentiable at x = 5.
ACCORDING TO QUES, Therefore, f(x) is not differentiable at \[x\text{ }=\text{ }5.\]
SOLVE:
According to ques, FUNCTION is differentiable at \[x\text{ }=\text{ }2.\]
SOLVE:
NOW ACCORDING TO QUES, AND, HENCE DIFFERENTIABILITY AT \[x\text{ }=\text{ }0.\]
SOLVE:
SO, f(x) is not differentiable at \[x\text{ }=\text{ }2.\]
Show that the function f (x) = |sin x + cos x| is continuous at x = p. Examine the differentiability of f, where f is defined by
Given, \[f\left( x \right)\text{ }=\text{ }\left| sin\text{ }x\text{ }+\text{ }cos\text{ }x \right|\text{ }at\text{ }x\text{ }=\text{ }\pi \] Presently, put \[g\left( x \right)\text{ }=\text{...
Find all points of discontinuity of the function:
Now, if f(t) is discontinuous, then \[2-\text{ }\text{ }x\text{ }=\text{ }0\Rightarrow x\text{ }=\text{ }2\] And, \[2x-\text{ }\text{ }1\text{ }=\text{ }0\Rightarrow x\text{ }=\text{...
Given the function f (x) = 1/(x + 2) . Find the points of discontinuity of the composite function y = f (f (x)).
fun wont be define and continuous \[2x\text{ }+\text{ }5\text{ }=\text{ }0\Rightarrow x\text{ }=\text{ }-5/2\] hence,\[x\text{ }=\text{ }-5/2\] is the point of discontinuity.
Find the values of a and b such that the function f defined by following function is a continuous function at x = 4.
So, \[-1\text{ }+\text{ }a\text{ }=\text{ }a\text{ }+\text{ }b\text{ }=\text{ }1\text{ }+\text{ }b\] \[-1\text{ }+\text{ }a\text{ }=\text{ }a\text{ }+\text{ }b\text{ }and\text{ }1\text{ }+\text{...
Prove that the function f defined by following equation remains discontinuous at x = 0, regardless the choice of k
Since the left hand limit is not equal to the right hand limit and both have constant values. so the given function remains discontinuous at \[x\text{ }=\text{ }0.\] ...
Find the value of k so that the function f is continuous at the indicated point:
ACCORDING TO QUES,
Find the value of k so that the function f is continuous at the indicated point:
HENCE K IS \[1\]
Find the value of k so that the function f is continuous at the indicated point:
\[~k\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]
Find the value of k so that the function f is continuous at the indicated point:
So, \[7\text{ }=\text{ }2k\] \[k\text{ }=\text{ }7/2\text{ }=\text{ }3.5\] SO VALUE OF K IS \[3.5\]
Find which of the functions if is continuous or discontinuous at the indicated points: f (x) = |x| + |x – 1| at x = 1
And hence, f(x) is continuous at \[x\text{ }=\text{ }1.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is continuous at \[x\text{ }=\text{ }1.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is discontinuous at \[x\text{ }=\text{ }0.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is continuous at \[x\text{ }=\text{ }0.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is continuous at \[x\text{ }=\text{ }0.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
at \[\mathbf{x}\text{ }=\text{ }\mathbf{4}\] And hence, f(x) is discontinuous at \[x\text{ }=\text{ }4.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
at \[\mathbf{x}\text{ }=\text{ }\mathbf{2}\] And hence, f(x) is continuous at \[x\text{ }=\text{ }2.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
at \[\mathbf{x}\text{ }=\text{ }\mathbf{2}\] And hence, f(x) is discontinuous at \[x\text{ }=\text{ }2.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
at \[\mathbf{x}\text{ }=\text{ }\mathbf{0}\] NOW, HENCE, given function f(x) is discontinuous at \[x\text{ }=\text{ }0.\]
Examine the continuity of the function f (x) = x3 + 2×2 – 1 at x = 1
since, \[y\text{ }=\text{ }f\left( x \right)\] will be continuous at \[x\text{ }=\text{ }a\] if, hence, f(x) is continuous at $$ \[x\text{ }=\text{ }1.\]